
Melt butter, flour, onion powder, garlic powder, and cayenne pepper over medium heat in a saucepan. Cook 1 minute.
Stir in milk and beer a bit at a time, whisking until smooth after each addition. Continue cooking over medium heat, add in mustard and Worcestershire, cooking sauce until thick and bubbly.
Reduce heat to low, add cheeses, and stir just until melted and smooth.
Serve warm with vegetables, tortilla chips or soft pretzels.