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 chicken broth and beer; simmer
until vegetables are tender, about 12 minutes.
Remove from heat.
Meanwhile, heat butter in a large soup pot over
medium-high heat. Stir in flour with a wire whisk;
cook, stirring until the flour is light brown,
about 3 or 4 minutes. Gradually stir in milk,
whisking to prevent scorching, until thickened.
Remove from heat, and gradually stir in cheese.
Stir beer mixture into cheese mixture. Stir in
Dijon mustard, Worcestershire sauce, and dry
mustard. Adjust for hot pepper sauce. Bring to a
simmer, and cook 10 minutes. Serve topped with