Make a Roux – In a medium saucepan, melt the butter over medium heat. Add the flour and whisk to combine. Cook until the roux turns blonde, about 1 minute.
Bloom the Spices - Add the garlic powder, onion powder, salt, and smoked paprika. Whisk and cook until fragrant, 15 to 30 seconds.
Add the Liquids - Gradually whisk the milk, then the beer, whisking continuously to break up any clumps of flour. Whisk in the Worcestershire sauce and mustard. Cook until the sauce is smooth and thickened; a few bubbles should break the surface, about 3 to 5 minutes.
Add the Cheese - Turn off the heat, then whisk in the cheddar cheese, stirring until smooth. For a thinner consistency, add more warm milk, 1 tablespoon at a time.
To Serve - If needed, rewarm the sauce over low heat before serving. Transfer the beer cheese dip to a serving bowl. Serve warm with pretzels or desired dippers.
Notes
Recipe Yield: About 2 cups
Serving Size: 1/4 cup
Beer Options: Use a wheat beer, lager, pilsner, or pale ale. Avoid IPAs, brown ales, or stouts.
Thinner Sauce: Use 2% or whole milk. Alternatively, reduce the butter and flour to 3 tablespoons each.
Cheesier Sauce: Add up to 3 cups of grated cheese.
Store: Transfer the cooled cheese dip to an airtight container. Refrigerate for up to 5 days. Reheat on the stove or microwave until warm. Add milk if needed to thin the sauce.