In a microwave-safe 2-quart casserole, combine butter and onion. Microcook, covered, on 100 percent power (high) for 3 to 4 minutes or until onion is tender, stirring once. Stir in flour. Stir in broth and milk. Cook, uncovered, on high for 4 to 6 minutes or until thickened and bubbly, stirring every 2 minutes until mixture starts to thicken. Cook, uncovered, for 2 minutes more, stirring every 30 seconds. Add cheese, a little at a time, and pepper; stir until cheese is melted. Serve in bowls as above.