In the same skillet, melt the butter and sauté the garlic until fragrant, about 1 minute. Stir in the flour and cook for another minute to form a roux.
Gradually whisk in the milk and chicken broth, ensuring there are no lumps. Cook until the sauce thickens, about 5 minutes.
Add the Parmesan cheese, salt, pepper, and Italian seasoning, stirring until the cheese melts and the sauce is smooth. Stir in the heavy cream or sour cream.