Cook linguine or fettuccine according to package directions, adding the broccoli for the last 5 minutes of cooking. Drain well.
Meanwhile, lightly coat a large skillet with nonstick spray coating. Add onion to the skillet. Cook, covered, over medium-low heat about 10 minutes or until tender, stirring occasionally.
In a small bowl stir together milk, cornstarch, bouillon granules, pepper, and nutmeg. Add to onion in skillet. Cook and stir over medium heat until thickened and bubbly. Cook and stir for 2 minutes more. Stir in wine and cheese until cheese is melted. Pour cheese mixture over pasta and broccoli; toss to coat. Makes 5 side-dish servings.