In a large kettle, cook onion in butter until soft. Blend in flour and seasonings; gradually stir in broth, milk and beer. Cook over medium heat, stirring constantly, until mixture comes to a boil; boil and stir until thickened. Add cheese, stirring and heating until smooth.
You can garnish with popcorn, croutons, minced parsley, chives or crumbled crisp bacon.