Make sauce: To same skillet over medium heat, add butter. Let melt, then add remaining garlic and cook until fragrant, 1 minute. Add flour and cook until golden, 2 minutes more. Whisk in milk and simmer until thick and creamy, 3 minutes, then stir in 1 cup mozzarella and all of the Parmesan. Spoon a thin layer of sauce onto the bottom of an 8"-x-8" baking dish.