In a 4- to 5-quart pan, combine onion, butter, and nutmeg. Stir often over high heat until onion is limp, 3 to 4 minutes.
Mix the cornstarch smoothly with a little of the chicken broth. Add to pan along with remaining broth, wine, pumpkin, and rice. Stir mixture over high heat until boiling, 3 to 4 minutes. Cover and remove from heat; let stand 5 minutes.
Stir in 3/4 cup cheese. Sprinkle portions with additional cheese and add salt and pepper to taste.