Melt butter in a large saucepan over medium-high heat; saute garlic until golden, 2 to 3 minutes. Lower heat to medium and gradually stir flour into garlic-butter mixture until dissolved and smooth, 3 to 5 minutes.
Gradually stir Parmesan cheese into garlic-flour mixture until cheese is melted and mixture is thickened, 2 to 3 minutes. Slowly pour milk into cheese mixture, stirring constantly, until smooth, about 5 minutes; season with Italian seasoning, salt, and pepper. Cook and stir until sauce reaches desired consistency, 5 to 10 minutes.
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