Multiplication in classes

Someone cooked on Shabbat for a sick person who is in danger and added more for him as well. According to the Rabbi, this is a Torah prohibition. Is it a prohibition of “multiplying in several portions” or a prohibition of cooking on Shabbat?
If it is a prohibition of cooking on Shabbat, is he obligated to do so or is he exempt from punishment but forbidden by the Torah?

I don't recall that a source is cited for this prohibition (especially since there are opinions that it is from the rabbis). Therefore, it is unlikely that it is an independent prohibition. There is an explanation and source for half a shiur (all milk is fat). Therefore, it is likely that it is a prohibition against cooking on Shabbat. In any case, it is also likely that he will be stoned, since anyone who cooks on Shabbat is stoned.

When one accidentally cooks twice the obligatory amount, one is not obligated to commit two sins, so the obligation is on the action and not on the quantity. So why would one be obligated when one multiplies the two shiurs under pikuach nefesh? That is why I thought that perhaps this is an independent prohibition, but as the rabbi said, it has no source. Perhaps it could be said that what one cooked for pikuach nefesh is not considered cooking because Shabbat was permitted under pikuach nefesh, and then the increase in the shiur added a new cooking act? Although even if we say that Shabbat was permitted, it is still clear that he simply cooked with permission, so the increase in the shiur did not add a new cooking act.

Maybe the rabbi didn't see the question?

I answered and now I see that it does not appear. Strange. I will write again.
Your evidence that it is a prohibition of action is incorrect. What is not required is two for double cooking because it is one ilm. This is a law in the laws of division for sins and not within the limits of the prohibition of cooking. Therefore, one is required even if it is a prohibition for the result. (By the way, in another article I argued that the obligation of sin is for the ilm and not for the offense).
Simply put, the prohibition is not for the action but for the result. However, the one who is obligated is the one who placed it on the fire (this is a condition for the obligation and not the prohibition itself). In any case, there is no reason not to require it for the multiplication.
In our case, only one prohibition has passed, because the first shiur that was cooked for the patient is a permissible act, and therefore the division for sins is not relevant here. There is cooking of the second shiur and therefore it is obligatory.

Thank you. And do those who disagree with the ruling believe, as I wrote, that it is a prohibition on the action, or does everyone agree that the prohibition is on the result?

It is likely that they disagree with this, otherwise there really is no reason why there should not be a Torah prohibition. Although it should be rejected.
In a response that did not appear, I commented that there is room to link this to the recent discussion regarding placing on the fire on Shabbat and cooking on Moshe (and also on the Sabbath). Although this too should be rejected.