In a small pot or saucepan over medium heat, melt the butter. Sprinkle in the flour and whisk to combine, a light paste will form. Cook, stirring constantly for about 1 minute.
Whisking constantly, slowly pour in the beer in a steady stream. Next, while whisking constantly, slowly add the milk.
Stir in the mustard, Worcestershire sauce and garlic powder. Cook over low heat for 1-2 minutes or until the mixture starts to thicken.
Remove from the heat and add half of the shredded cheese into the sauce. Stir until the cheese is completely melted. Add the remaining cheese and stir until it melts and the dip is smooth. Season to taste with salt and ground black and serve immediately.
Notes
Best Texture: For the smoothest, most luxurious cheese dip, use cheese shredded from a block of cheese. Pre shredded cheese can be used, just keep in mind that this type of cheese melts differently due to additives that prevents the shreds of cheese from clumping up. That said, I've used it many times with great results.
Extra Richness: For an extra rich dip, use half and half.
Flavor Twist: For a fun flavor twist, add 1/2 can of rotel tomatoes or roasted tomatoes and green chiles and a bit of cumin. Viva la Tex Mex cerveza queso dip!
Keep it Warm: To keep this appetizer warm longer, serve the dip in a fondue pot or small crockpot.
Storing: Leftover beer cheese dip (if you have any) can be stored in the refrigerator for 3-4 days.
Reheating: Reheat in the microwave, in small intervals, stirring after each interval. You can also reheat over low heat, stirring as needed. If warming up on the stove top, you may need to stir in a bit of milk to loosen the sauce a bit.