Whisk together butter, garlic and half & half in a medium saucepan over medium heat. Bring to a simmer (do not boil), then remove from heat.
Stir in cheese, a handful at a time. Gently stir until the cheese melts before adding the next handful.
Return pan to burner over medium heat. Season sauce with salt and pepper. Stir until cheese sauce is smooth and the sauce is thick enough to coat the back of a spoon. Remove pan from heat and allow sauce to cool for 5 minutes. Alfredo sauce will thicken even more as it cools.
Serve and enjoy!
