In a 5- to 6-quart pan over medium-high heat, frequently stir onion in butter until lightly browned, about 5 minutes. Add nutmeg and flour; stir until lightly browned, about 2 minutes.
Remove from heat and whisk in milk and broth. Stir over high heat until boiling; reduce heat and boil gently, stirring often, until sauce is reduced to 4 cups, about 10 minutes. Use hot or cold.
Nutritional analysis per 1/2 cup.