Combine 3 tablespoons oil and 1 tablespoon butter in a large skillet; place over medium-high heat until butter melts. Add onion, garlic, and mushrooms; sauté 3 minutes or until tender, stirring constantly. Remove mushroom mixture; keep warm. Wipe skillet with a paper towel.
Add remaining 1 tablespoon oil and 1 tablespoon butter to skillet; place over medium-high heat. Add rice, and sauté 1 minute. Reduce heat to medium. Add rosemary, nutmeg, and 2 1/2 cups broth, stirring constantly, until liquid is absorbed. Add remaining broth, 1/2 cup at a time, until absorbed. (Total cooking time is about 40 minutes.) Stir in mushroom mixture. Add wine; cook, stirring gently, until absorbed. Stir in pepper, cheese, and, if desired, salt. Serve immediately.