Melt the butter in a medium saucepan over medium heat. Add the minced garlic and cook, stirring often, until fragrant, about 1 minute. Whisk in the milk, flour, and grated cheeses. Cook the milk mixture, stirring occasionally, until the sauce begins to simmer and thicken. Season to taste with ground black pepper and salt. Remove from heat.rn Serve immediately or place in a mason jar and refrigerate for later.