Melt the butter in a large saucepan over medium heat. Add carrots, celery, and onion, and sauté until tender, about 5 minutes.
Whisk in flour, salt, and pepper until smooth. Cook for 2 minutes, stirring constantly.
Gradually whisk in chicken broth, milk, and beer. Bring to a gentle simmer and cook until thickened, about 10 minutes.
Reduce heat to low. Stir in Cheddar cheese, Worcestershire sauce, mustard powder, and hot sauce until cheese is melted and soup is smooth.
Serve hot, garnished with crumbled bacon on top.