Use coarse stone-ground cornmeal for the best texture; avoid instant cornmeal or grits. Always grate your own cheese, as pre-grated cheese contains anti-caking agents that prevent smooth melting. Remove the pan from heat before adding cheese to ensure it melts smoothly without separating. If the polenta becomes too thick, add more broth or milk a splash at a time. Polenta thickens as it cools, so keep it slightly looser than desired when serving.