Create a roux: In a large pot, melt butter over medium-high heat. Add in minced garlic and sauté until all the butter is melted. Sprinkle in the flour and whisk constantly for 1 minute. Slowly pour in the milk, whisking until well combined.
Mix: Add in all the other ingredients one at a time, whisking until thickened and the cheese is fully melted and glossy. When you stir it, it should stream like ribbons!
Serve: Serve beer cheese warm or room temperature with crusty bread, pretzels, crackers, or veggies.