Utensils into which cold ĥametz has been placed do not require hagala in boiling water; a thorough washing is sufficient to kosher them for Pesaĥ. For example, beer mugs become kosher for Pesaĥ by means of a thorough washing, even though beer is ĥametz gamur, because as long as the ĥametz in a utensil has not reached the temperature of yad soledet, the utensil does not absorb the taste of its contents. Certainly, then, a cake plate used for ĥametz can be koshered for Pesaĥ with a thorough washing, because in addition to the fact that cookies never reach yad soledet, they are dry, and taste does not transfer to a utensil without a liquid medium.
But if beer is left in a mug for more than twenty-four hours, kvisha (“pickling,” or the absorption of taste through prolonged soaking) occurs, and the taste of the ĥametz gets absorbed into the glass based on the Sages’ rule: “kavush ke-mevushal” (pickling is akin to cooking). Therefore, it is forbidden to use such a utensil on Pesaĥ unless it has been koshered.
Utensils that have absorbed taste via kvisha can certainly be koshered through hagala in boiling water; if hagala is effective on utensils that absorbed via cooking, it certainly works on utensils that absorbed via kvisha. Moreover, since kvisha is a milder form of absorption, one may kosher such a utensil by soaking it in water for three twenty-four hour periods: First, one places the utensil in water and leaves it there for twenty-four hours. Second, the water is changed and the utensil is left there for another twenty-four hours. Then the water is changed once again, and the utensil soaks for a final twenty-four-hour period. Nevertheless, this method of koshering is generally not helpful because it is faster and easier to perform hagala with boiling water. But when dealing with utensils that are liable to be damaged by boiling water, soaking in water for three twenty-four-hour periods can be a very useful solution.
It is also worth mentioning that when it comes to alcoholic beverages such as whiskey, some poskim are of the opinion that the taste of the ĥametz is absorbed by the glass in a mere eighteen minutes. Thus, if one wishes to use such a glass on Pesaĥ, it must first be koshered using one of the aforementioned methods.
Even though an earthenware utensil that absorbed ĥametz during the cooking process cannot be koshered through hagala, if such a utensil absorbed the taste through the pickling process, it can be koshered through hagala or through soaking for three days, as per SA 451:21. See also MB ad loc. 118 and Kaf Ha-ĥayim 242, which state in the name of Shakh YD 135:33 that the leniency of permitting one to kosher an earthenware vessel that absorbed forbidden taste via pickling applies only to ĥametz and not to other forbidden foods.