In a large saucepan over medium heat, stir together carrots, onion and garlic. Stir in cayenne pepper, and salt and pepper. Pour in chicken broth and beer, simmer until veggies are tender, remove from heat (about 12-15 minutes).
Meanwhile, heat butter in large soup pot over medium heat. Stir in flour with a wire whisk. Cook, stirring until the flour is light brown, about 4 minutes. Gradually stir in milk, so it does not scorch, until thickened. Remove from heat, and stir in cheese, keeping warm.
Stir beer mixture into cheese mixture. Stir in Dijon and Worcestershire sauce. Bring to simmer, cook 10 minutes.