In a saucepan over medium heat, melt the butter. Whisk in the flour and cook for about 1 minute until slightly golden.
Slowly pour in the beer while whisking constantly, followed by the milk. Stir until smooth and slightly thickened.
Add the Dijon mustard, Worcestershire sauce, garlic powder, smoked paprika, and cayenne pepper. Stir well.
Gradually add the shredded cheeses, stirring constantly until fully melted and smooth.
Taste and adjust with salt and black pepper if needed. Serve warm with pretzels, bread, or veggies.
