As we learned (section 2), the difference between pots used for cooking, which are kashered by means of hagala in boiling water, and baking trays and roasting spits, which are used for baking and roasting and are kashered by means of libun, is that the absorption through cooking is mild, whereas absorption through fire is intense. This is because the objective of cooking is to mix together the liquids in the dish, so it becomes softer and more flavorful. Since cooking is liquid-based, its absorption is milder. In contrast, the objective of baking and roasting is to minimize the liquid in the food, thus hardening it. Therefore, its absorption is more intense.
Even if a dish cooked in a pot was burned, the pot is kashered by means of hagala, since the initial absorption was through liquid, and, moreover, we follow the main purpose of the kli, which is made for cooking, not baking (Rosh).
Accordingly, a skillet or frying pan is kashered by means of hagala, because the purpose of the oil placed in the frying pan is to make the food more liquid. This is the difference between baking and frying: baking dries out the pastry, whereas frying makes it more liquid. This is the view of most Rishonim (Rosh, Raavyah, Mordechai, and Sha’arei Dura).
But some say that since people often fry with small amounts of oil, the oil is often used up, and the absorption is dry, via fire. Moreover, sometimes there are parts of the frying pan that were not coated in oil even initially, and there the absorption is by means of fire. Therefore, a frying pan or skillet has the same status as a baking tray, and it is kashered by means of libun (Rashba, Rabbeinu Yoel).
In practice, one may kasher a skillet or frying pan for Pesaḥ by means of hagala. Le-khatḥila it is best to kasher it with light libun, which is how it is used all year. This is also the easiest way to kasher it, as it entails heating up the empty skillet until it reaches the temperature of light libun (as described in the next section; regarding Teflon skillets, see section 9 below).
The Rishonim do not distinguish between Pesaḥ and other prohibitions, but SA (YD 121:4; 451:11) is stringent with regard to other prohibitions, requiring libun, but lenient with respect to Pesaḥ, ruling that hagala is sufficient. The Aḥaronim explain that with regard to Pesaḥ R. Karo combines the opinion that hagala is sufficient with the view that ḥametz before Pesaḥ is considered a permitted food (above, section 3), and thus rules leniently that one may kasher a frying pan for Pesaḥ via hagala (Gra, Ḥok Ya’akov, Ḥida, Ma’amar Mordechai, Nahar Shalom, Erekh Ha-shulḥan, and many others). Against them, Pri Ḥadash (YD 121:8) states that since, in practice, we rule that ḥametz absorbed before Pesaḥ is considered a prohibited food, kashering a skillet for Pesaḥ requires heavy libun. This is also the view of Pri To’ar.
According to Rema (451:11), technically one may kasher a skillet for Pesaḥ by means of hagala, but it is proper to be stringent and kasher it by means of light libun. This is the practice le-khatḥila. (Regarding light libun, see the next section.)
Some say that when there is no sizzling, bubbling oil in the skillet, the skillet has the status of a baking tray (Pri Ḥadash 451:11, SAH 36). It seems from the Rishonim that even if the skillet was coated with a bit of oil, since the oil is supposed to be absorbed into the food as part of the frying process, unlike baking, which is supposed to dry out the food, it is kashered by means of hagala (Rosh and others; so states AHS 451:13. Kaf Ha-ḥayim 451:70 gives a different parameter – that if there was enough liquid present in the skillet to coat something that touched something that was in the skillet [“tofei’aḥ al menat le-hatfi’aḥ”], the skillet can be kashered by hagala).
Regarding a pot used to prepare jachnun, kugel, or kubana, or a frying pan used to prepare malawach, I initially thought that if no sizzling oil is placed in them, they are kashered by means of libun. In practice, however, it seems to me that the result is determinative: If the food remains moist, as in the case of kugel, it is considered “cooked,” and the kli is kashered by means of hagala. If the result is more pastry-like, as in the case of typical kubana and malawach, the kli is kashered by means of libun. If the result is something in between, as in the case of soft kubana and jachnun, one may kasher them by means of hagala, as we can factor in the opinion that ḥametz before Pesaḥ is considered a permitted food, as explained in section 3 above. (See Peninei Halakha: Berakhot 6:11, n. 10.)