Allow cheddar cheeses to stand at room temperature for 30 minutes. Meanwhile, in a 4-quart Dutch oven heat butter over medium heat until melted. Add chopped onion, carrot, green onions, and garlic. Cook for 8 to 10 minutes or until vegetables are tender, stirring occasionally.
Stir in flour and dry mustard (mixture will be thick). Gradually stir in broth. Cook and stir until bubbly. Add beer and cream; stir in hash brown potatoes and broccoli. Bring to boiling; reduce heat. Simmer, uncovered, for 5 minutes, stirring occasionally.
Gradually stir in cheddar cheeses, stirring after each addition until cheeses are melted. Stir in bacon, Parmesan cheese, hot pepper sauce, and Worcestershire sauce.