Melt the butter in a saucepan over medium heat. Add garlic and cook for about a minute until the garlic becomes fragrant.
Stir in flour until combined with the butter and starting to get slightly brown; about one minute. Gradually whisk in milk and half & half and cook, stirring constantly, until the mixture is smooth and starting to thicken.
Stir in cream cheese until melted, about 1-2 minutes. Then add Parmesan cheese. If the mixture is too thick, add additional milk as needed.