Start by shredding 1 ½ cups sharp cheddar cheese and 1 cup smoked gouda cheese and setting them aside.
In a medium saucepan or braiser pan, melt ¼ cup unsalted butter over medium-low heat. Once melted, add ¼ cup all-purpose flour, a little at a time, and whisk into the melted butter until a roux forms. Continue whisking to cook the flour until a blonde roux forms, about 2 minutes.
Slowly pour in 1 cup half-and-half and ⅔ cup beer, whisking constantly until a thick but smooth looking sauce forms. Do not let it become hot enough to bubble and simmer.
Add 1 teaspoon Worcestershire sauce, 1 teaspoon mustard powder (or Dijon), ½ teaspoon garlic powder, ½ teaspoon onion powder, ¼ teaspoon smoked paprika, ⅛ teaspoon cayenne, and ½ teaspoon salt and whisk to combine thoroughly.
Lower the heat and add in the shredded cheddar and smoked gouda. Whisk or stir together until the cheese has melted, and the beer cheese is fully combined and smooth.
The beer cheese dip will continue to thicken as it cools. If you would like it a bit thinner, add some more beer or half-and-half. Pour the cheese sauce into a serving bowl for dipping and serve warm. Alternatively, add to a small slow cooker to transport and keep warm while serving.
Notes
1) Cheese – Read the above post for more cheese options. Whatever cheese you use, however, I recommend shredding your own. It tastes and melts better and literally takes about a minute to shred.2) Beer – The above post has more information on beer options but look for a full-bodied yet mild and crisp beer without strong flavors. Good options include American style pilsners and most lagers. I checked at a local convenience store for decent options that I could buy in a single can.