In a 5- to 6-quart pan, mix polenta and flour. Stir in broth and cream, mixing well. Bring to a boil over high heat, stirring often with a whisk or spoon to prevent lumps and sticking. Reduce heat; simmer uncovered, stirring often, until polenta feels creamy and smooth to taste, 15 to 20 minutes.
Stir butter and half the cheese into polenta; ladle into bowls. Sprinkle remaining cheese over polenta and add salt and pepper to taste.