The Shulhan Aruch, in Siman 318, permits reheating a "Pashtita"-a doughy dish filled with fat-on a Blech. Since the Pashtita, including the fat, are already cooked, the principle of "En Bishul Ahar Bishul" (There is no prohibition to re-cook/or re-bake solid foods) applies. Even though the fat will melt when heated, Maran does not consider the Pashtida a liquid, which may not be reheated. Neither is he concerned that transforming the solid fat into a liquid constitutes the prohibition of Nolad or Sehitat Perot (squeezing juice out of fruit).
Therefore, a solid food with congealed fat in the refrigerator, may be reheated on the Blech on Shabbat. However, the Rema records that Ashkenazim are strict on this matter.
Hacham David adds that there is no difference between fat which originated as a solid and a gravy which originated as a liquid and then congealed. Both may be reheated and transformed back to a liquid. However, a liquid soup or water which was frozen into solid icy cubes retains its status as a liquid and may not be reheated on Shabbat. It is not considered a solid, because it reverts to a liquid when left alone at room temperature, whereas the fat and congealed gravy become liquid only when heated.
One may reheat congealed fat and gravy on a Blech, but not frozen soups.