Shred all the cheeses and set them aside for later use. Mix garlic powder, onion powder, cayenne pepper, salt, and pepper in a small bowl and reserve. Warm the milk in the microwave for about 45 seconds.
In a medium-sized skillet, preferably a 10-inch cast iron, melt the butter over medium heat. Whisk in the flour and cook for 1 minute, stirring constantly. Gradually add the milk, followed by the beer, whisking continuously to maintain a smooth consistency.
Stir in the prepared seasoning mix, Worcestershire sauce, and Dijon mustard. Allow the mixture to come to a gentle simmer, adjusting the heat as needed, and let it bubble and thicken for approximately 5 minutes.
Lower the heat and allow the base to cool slightly. Gradually incorporate the shredded cheeses, stirring until melted and smooth. Adjust the thickness and flavor by adding a splash more beer, if desired. Taste and season with additional salt or pepper if needed.
Serve immediately with your choice of soft pretzels, crusty bread, fresh vegetables, or chips.