Melt the butter in a medium-sized saucepan over medium heat, then add the minced garlic and sauté until its aroma deepens, about 1–2 minutes, before whisking in the flour. Remove the pan from the burner and briskly whisk in 2 tablespoons of the milk until the mixture is smooth, then incorporate another 2 tablespoons of milk in the same manner. Gradually add the remaining milk in three parts, whisking thoroughly between each addition to maintain a lump-free consistency. Stir in the beer, dijon mustard, cayenne pepper, and salt, then return the pan to the heat, stirring steadily until the sauce thickens and begins to bubble, approximately 2–3 minutes. Take the pan off the heat once more, adding the grated cheese a handful at a time and whisking well after each addition until fully melted and velvety. Taste and adjust with extra salt and a touch more cayenne if desired. Sprinkle with a pinch of cayenne and chopped parsley for garnish. Present warm with pretzels, bread, chips, or assorted vegetables.