Bring broth and 1 cup water to a simmer in a medium saucepan (do not boil). Keep warm over low heat.
Heat oil in a large Dutch oven over medium heat. Add onion to pan, and cook 5 minutes or until tender, stirring frequently. Add rice; cook for 2 minutes, stirring constantly. Stir in 1 1/2 cups Champagne; cook 2 minutes or until liquid is nearly absorbed, stirring constantly. Stir in broth mixture, 1/2 cup at a time, stirring constantly until each portion is absorbed before adding the next (about 20 minutes total). Remove from heat.
Stir in remaining 1/2 cup Champagne, radicchio, 1/2 cup cheese, butter, salt, pepper, and nutmeg. Let stand 5 minutes. Serve with remaining 1/2 cup cheese.