Heat a medium saucepan over medium-low heat and add butter, flour, and minced garlic. Whisk to combine, and continue to cook for 3 minutes while the roux cooks. At this point, the garlic should be very fragrant and the roux should begin to darken in color slightly.
Begin to stir in the milk a few splashes at a time. Ensure each batch fully incorporates into the flour mixture prior to adding more. Continue until all milk has been added. Heat the sauce to a gentle simmer.
Add Parmesan cheese a handful at a time, stirring fully into the sauce until you have a smooth and creamy consistency.
Add salt and pepper.
Remove from heat and serve over fettuccine noodles with sliced chicken breasts to create your own homemade chicken fettuccine alfredo.
