Bishul 26 - Ain Bishul Acher Bishul - 6; Liquids 2 (Klal 20 Siman 8) S0523

We are continuing in siman 8, discussing the concept of bishul achar bishul as it applies to a davar lach. The Chayei Adam discusses a case of something fully cooked; meaning, he is not currently discussing a case of something which has not yet been fully cooked and is in the process of being cooked for the first time. Rather, he is discussing whether it will be assur to reheat or recook a davar lach, once fully cooked, because of the concept of ain bishul achar bishul. 
We have learned that once a davar yaveish is fully cooked, we pasken that ain bishul achar bishul. When it comes to a davar lach, he writes that there are opinions that ain bishul achar bishul as well, but we pasken that yeish bishul achar bishul. He explains that when it comes to liquid, heating the liquid is significant, because people tend to prefer cooked liquids hot, so reheating is considered cooking the liquid.  When it comes to a solid, the temperature of the food is less significant, and reheating is not so important, and therefore ain bishul achar bishul

We will now see the text of the Chayei Adam inside. The Chayei Adam writes that if davar lach is no longer boiling but is still yad soledes bo from its original cooking, there is no concern of bishul achar bishul, because it is still looked at as being part of the original bishul. To that end, one could perform chazarah with it (assuming the other criteria are met). If the food has cooled to below yad soledes bo, some poskim hold there is no issue of yad soledes bo, because as long as the item was fully cooked the first time, it remains in a cooked state. However, others hold that it is considered bishul, and we would apply the issur of ain bishul achar bishul.
Since it is a machlokes, the Mishnah Berurah paskens that one must be machmir and be concerned for the possible issur deoraysa. At the same time, since it is a machlokes, the Chayei Adam will quote the Rema who holds that even if the davar lach has cooled to lower than yad soledes bo, one can be meikil and reheat the davar lach as long as it has not cooled down to room temperature. We will need to explain why we can be meikil in the face of a safeik issur deoraysa. We also need to clarify since one can take something at room temperature (or colder) and warm it to under yad soledes bo, so arguably, one should be able to warm up this food to under yad soledes bo, and then, since it is now warm, heat it above yad soledes bo. Is that true? We will discuss these questions in the upcoming shiurim, be’ezras Hashem.

Summary
Bishul achar bishul regarding a davar lach will depend on the state of the food. If the food is anywhere between maachal ben derusai and mevushal kol tzorcho, we are machmir for bishul achar bishul to cook it further. 
However, if it is fully cooked, as long as it has not cooled to room temperature it will not be assur to return it to the heat source. This is known as chazara, and is dependent on a few other criteria as well.