Chicken stock gives the polenta a richer flavor. If you use canned stock, you may not need to add any salt.
Bring stock or water, milk, and herbs, if using, to a boil in a small, deep saucepan over medium heat. Lower heat and slowly sprinkle in cornmeal, stirring constantly. Cook, stirring constantly, for 20 minutes over low heat. If polenta becomes too thick, add up to 1 more cup of boiling liquid. Polenta should resemble a thick porridge. Add salt to taste. Stir in butter.
Pour polenta onto a 9-by-13-by-1/2-inch baking sheet and smooth out. Cover with plastic and refrigerate until firm, or overnight.
Cut polenta into 8 triangles and saute in butter in a nonstick skillet, or grill until heated and brown on both sides.