In a 4-quart Dutch oven melt butter over medium-high heat. Add broccoli, carrots, and onion. Cook and stir 5 minutes or until vegetables are soft.
Stir flour, dry mustard, and pepper into vegetables. Add milk all at once. Cook and stir until thickened and bubbly. Cook and stir 1 minute more. Add cream cheese. Stir in sausage, cheddar cheese, broth, and beer. Cook and stir over low heat until cheese melts and soup is heated through.