Cooked polenta can have two distinct textures. Served just after making, polenta makes a creamy bed for toppings such as crisp asparagus. Cooled polenta is firm enough to slice and then grill or bake for other dishes. Storage tip: The remaining polenta can be stored in the refrigerator for up to 3 days. Spread it into an oiled 9-inch baking pan, let cool and cover tightly with plastic wrap.