Cut onions into thin slices; separate into rings. Place onion rings in an ungreased 1-1/2 quart casserole. For the white sauce, melt butter in a small saucepan; blend in flour, and gradually stir in milk. Cook, stirring constantly, until thickened. Add salt, pepper, and cheese; stir until cheese has melted. Pour sauce over onions. Bake, uncovered, at 325° about 45 minutes. Serves 4 to 6.