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 stock and beer; simmer until vegetables are tender, about 12 minutes. Remove from heat.
Meanwhile, heat butter in a large stock 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. Keep warm.
Stir beer mixture into cheese mixture. Stir in Dijon mustard, Worcestershire sauce and dry mustard powder. Adjust for hot pepper sauce. Bring to a simmer and cook 10 minutes. Serve topped with popcorn.