Chicken stock gives the polenta a richer flavor. If you use canned broth, 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 as much as 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.