Stir in 1 or 2 ladles of broth, or enough to cover rice. Stir over medium heat until broth has been absorbed. Continue cooking and stirring rice, adding broth a little at a time, about 10 minutes. During remaining 10 minutes of cooking, add champagne 1 cup at a time instead of broth. Do not add more champagne until previous amount has been absorbed.
Rice is done when it is tender but firm to the bite.
Season with salt. Place in a warm dish. Serve immediately with remianing cheese. Makes 6 servings.