After you have shredded the cheese, make the roux by melting the butter in a medium-sized saucepan over medium heat. Whisk in the flour until completely incorporated. Cook, stirring frequently, for 2 minutes.
Add the beer and stir until incorporated. Next, add the milk, Dijon mustard, Worcestershire sauce, paprika, salt, and pepper. Stir continuously, until the mixture begins to thicken and coats the back of a wooden spoon, usually about 3 to 5 minutes.
Sprinkle in the cheese and stir until melted. Taste and add more salt, if desired.
The sauce is ready to be served at this point. Once off the heat, it will thicken even more. Serve warm or at room temperature.
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Notes
We think a mild cheddar is wonderful for this sauce, but you can go with whatever is your favorite. Just make sure it is a good melting cheese. Sharp cheddar is great, too, but will deliver a stronger flavor. You can also use a combination of cheddar with Monterey Jack, mozzarella, or smoked Gouda.We go with a nice German lager, but, like the cheese, go with whatever is your favorite. Strong stouts and flavored beers will have a major impact on the taste, so experiment with it before serving to guests!The sauce is wonderful warm or room temperature. It can be made up to 3 days in advance, and gently reheated on the stove over low-medium heat.