In a 4-quart Dutch oven, melt butter over medium heat. Add onion, carrot, celery, and green onions. Cook and stir 8 to 10 minutes or until onion is golden.
Stir in flour and mustard. Cook and stir 1 minute. Add broth; cook and stir until bubbly. Stir in beer and whipping cream. Add potatoes. Bring to boiling; reduce heat. Simmer, uncovered, for 10 to 12 minutes or until potatoes are tender.
Slowly add cheddar cheeses, whisking until cheeses are melted. Whisk in Parmesan or Romano cheese, hot-pepper sauce, and the Worcestershire sauce.