Maaseh Shabbos 6

If one cooks on Shabbos or does etc. - and if it a melacha drabanan see the Pri Megadim who writes that it is the same rule [for Torah and Rabbinic laws that were transgressed] and if it was done by mistake you have to wait until after Shabbos, see there....

....and I searched and I found in the Biur HaGra that he writes and comes out practically that even the Shulchan Aruch who paskens like Rabbi Yehuda, that is only if one transgressed a Torah level prohibition, though by a Rabbinic prohibition he holds that we don't penalize the one who did it by mistake in order to prevent it from being done on purposeand he brings proofs for this from explicit gemaras, and so too the Rambam paskens that if one [ritually] immerses items on Shabbos by mistake he may use them, if he did so intentionally, he cannot use them until after Shabbos. [Though this needs deeper analysis, for the Gra writes there that Rabbi Yehuda agrees with Rabbi Meir if the melacha transgressed was Rabbinic in nature and it implies there that this is true whether it was transgressed by accident or on purpose, and so too it is implied by the Rambam who paskens that if one immerses the items intentionally he may not use them until after Shabbos, which implies that after Shabbos even he may use them, but why should this be true? The Rambam holds like Rabbi Yehuda that for transgressing a Torah level prohibition intentionally it is forbidden forever and even if the transgression was on a Rabbinic prohibition it should be the same, for Rabbi Yehuda holds that we don't fine one who transgressed by mistake in order to prevent it from happening on purpose, but within the fine for one who transgressed intentionally we don't find in the gemara that Rabbi Yehuda makes a distinction between a dRabanan and a dOraysa? This needs more analysis]....

if one transgressed and left the food on the fire intentionally what is the law? -is it permitted to eat [on Shabbos] or not?

Hot water he did not prohibit - because further cooking is bad for it.

Eggs he forbade - since further cooking improves them.

was it not referring to that Shabbos itself? - that he forbade them to eat them.

No, it was for the following Shabbos - that he forbade them now, to dissuade them from doing it again the next Shabbos, though he permitted them to be eaten.

If one transgressed and left food on the fire what is the law? - to say that we are talking about when the food was not cooked enough to be edible under duress is incorrect, for we already answered that question earlier, saying that it was forbidden like Rav Nachman the son Yitzchak. It appears to the R"Y that the question was where it was cooked and it was by accident and according to Rabbi Yehuda, even though the halacha is not like Rabbi Yehuda, [the crux of the question being:] would he forbid fully cooked food that would improve with further cooking specifically if it was cooked intentionally, or maybe even if he further cooked it by accident [he would forbid it]? And we bring a proof from the story with Rabbi Yose who forbade it, which implied to him that even if it had been cooked by accident, since it says and it was left on the fire, and not and he left it on the fire [the first implying it was accidental, the second that it was done intentionally]. Though in truth the words "if he transgressed and left it on the fire" sound like he is doing so intentionally, like "if he transgressed and kneaded [dough] in Pesachim (42a). The Rashba says that the question is only before the decree was made, for once the decree was made it is obvious that by mistake is for forbidden just like when it was done intentionally.

and if he forgot it on a kirah whose fire was not cleared out or covered something which was not cooked enough, it is forbidden, and all the more so if he put it there intentionally, for Rav Shmuel the son of Yehuda says in the name of Rabbi Yehuda, in the beginning they said that one who cooks on Shabbos, if it was an accident then it may ne eaten, if it was done intentionally then it may not be eaten, and so too if he forgot it [on the fire] though once the number of people who left it on the fire on purpose but they claimed that they had done so by mistake grew, they made another decree even if one forgot it would be forbidden, and where one forgot something which was fully cooked but it would still improve with further cooking, this was the question of the gemara and it is not answered so we rule leniently and we don't forbid that food, since it is a doubt on a Rabbinic rule, so the rules say we deal leniently.

(1) 1. The Laws of Kirah and a Tanur, placing pots on them on Erev Shabbos: A Kirah is one which is constructed in the shape of a (large) kettle. Pots are placed on top of it, where it has its mouth, and there is room for placing two pots. If this Kirah was fired by means of Gefes [olive waste], or with wood, one may not place food on it to cook in the evening (on Erev Shabbos) with the intention of leaving it there (until after Shabbos arrives) – unless the food has already been fully cooked and is shrinking (i.e., continually getting bigger and smaller as a result from the cooking) to its detriment, in which case it need not be feared that the coals in the stove will be stirred. It is also permitted to place the pot on the stove if the food is raw, i.e. it has not been cooked at all. Since it is raw, one will not pay attention to it until the next morning, as it is can finish cook during the night without stoking the coals. However, if the food is cooked a little bit, or even if it is fully cooked but shrinking through cooking will benefit it, we are concerned that the coals might be stoked. Therefore, leaving it on the stove is forbidden unless the stove is raked, in other words, all the coals are removed from it or are covered with ashes, in other words the coals are covered with ashes to lessen the heat’s intensity. If a raw piece (of meat) is put into the pot, it is permitted just as if it would consist entirely of raw (meat), since now he will not pay attention to the entire pot. But even if the coals were not raked (meaning the coals were taken out of the oven) or covered with ashes (meaning the coals were covered with ashes) it is permitted to place a pot next to it, on the outside. If it was fired with straw or stubble, it is permitted to allow a pot to stay on it even if it was not Gerufa (raked from the stove) or Ketuma (the coals are covered with ashes). RAMA: If two Kirah stoves are joined one beside the other, with an earthenware partition between them: if one is Gerufa or Ketuma and the second is not Gerufa or Ketuma, it is permitted to allow a pot to stay on the one which is Gerufa or Ketuma, even though the one which is not Gerufa or Ketuma will add to its heat. However, as for a Tanur stove even if it was fueled by straw or stubble, it is forbidden to place (a pot) even adjacent to it – even if it is Garuf ve’katum RAMA as long as it is Yad soledes bo. (Haga'ot Mordechai) It goes without saying that it is forbidden to let a pot stay within it or on it. As for a Kupach-stove which has room for placing one pot on it, where it was fueled by straw or stubble, it has the status of a Kirah; where it was fueled by Gefes or wood, it has the status of a Tanur. (Our types of ovens have the status of a Kirah) (R"an). And if he forgot and left it (on the stove) if it is a Tavshil that is cooked all the way it is permitted even if it is food that improves as it condenses (called 'Mitztamech v'Yafeh Lo'). But if it is a dish that is beginning to cook and is not cooked all the way it is forbidden until Motzei Shabbos. Where one deliberately leaves a pot of food, it is forbidden in both cases RAMA: until a time period has elapsed (after Shabbos) during which the cooking done on Shabbos could be done (after Shabbos) (Ha'agahot Ashiri and Rambam). But if a Non-Jew puts it back on on Shabbos the law is the same as one who forgot and left it on (Ha'agahot Ashiri). And if a Jew puts it back on the law is the same as one who intentionally left it on. (Ha'agahot Mordechai). And if the food condensed through more cooking to its detriment it is permitted because he receives no benefit from the forbidden thing. (Beis Yosef, and see the beginning of Siman 237) There are those who say that where it has already been cooked to the degree of Ma’achal ben Derusa’i (i.e. the name of a thief who ate his food semi-cooked) or it is completely cooked and further cooking will improve it, it is permitted to leave it on a Kirah. RAMA: or even on a Tanur (HaMagid; Ha'agahot Mordechai; the beginning of the paragraph Kirah in the Beis Yosef) even one fired with Gefes (olive waste) or wood, and even if it was not Gerufa or Ketuma. In this opinion, Garuf ve’katum and firing with straw and stubble were mentioned only when the cooking process has begun but has not reached the stage of Ma’achal ben Derusa’i; or, where one has removed the pot from the stove and desires to return it on Shabbos. Where one forgets and leaves a pot of food, which has begun to cook, but has not reached the stage of Ma’achal ben Derusa’i , it is forbidden to eat it. It goes without saying where one intentionally leaves it there that it is forbidden to eat. RAMA: The people’s custom is to be lenient and follow this last opinion ...........