Long cooking yields the traditional, silky-smooth result. For quicker cooking, the night or morning before you wish to cook the polenta, bring 1 ½ cups water or broth to a boil in a large saucepan and whisk in the polenta. Cover and let sit for up to 12 hours. When ready to cook, add the remaining 2 ½ cups water or broth to the saucepan, whisk to break up the polenta, and simmer until thickened and the cornmeal has lost its raw taste, 10 to 12 minutes.

Bring to a boil in a large saucepan:

Pour in very slowly, whisking constantly:

Reduce the heat to low and cook, stirring frequently with a wooden spoon, until the polenta is thick and comes away from the sides of the pan as it is stirred and the cornmeal has lost its raw taste, 30 to 40 minutes. Stir in: