In a large saucepan over medium heat, stir together carrots, onion, celery, and garlic.
Stir in hot pepper sauce, cayenne pepper, salt, and pepper; pour in broth and beer; simmer until vegetables are tender. Remove pan from heat.
While the soup is simmering heat butter in a large soup pot over medium heat. Whisk in flour and cook, stirring until the flour is light brown. While continually whisking, add milk; keep whisking until thickened. Remove from heat, and gradually stir in cheese. Keep warm.
Stir beer mixture into cheese mixture. Add Dijon mustard, Worcestershire, and dry mustard. Bring to a simmer, and cook 10 minutes. Serve topped with Pretzel Pieces.