Preheat oven to 350 degrees F (175 degrees C).
Lightly grease 9×13 inch baking dish. Arrange potatoes over the bottom of the dish, and set aside.
Melt 1 tablespoon butter in a saucepan over medium heat. Add the garlic and onion; cook and stir until the onion is transparent, about 5 minutes. Stir in 3 tablespoons butter until melted. Sprinkle the flour, salt, and pepper over the onion mixture. Cook and stir until mixture bubbles and thickens, about 2 minutes. Continue to stir the flour mixture while gradually pouring in the milk and buttermilk, and return the mixture to boiling. Stir in 3/4 cup Parmesan cheese; cook for 2 minutes until melted, and mixture is smooth. Pour the mixture over the potatoes in the baking dish, stirring to coat evenly.
Bake in preheated oven for 1/2 hour, and stir. Bake 1/2 hour longer, stir the potato mixture again, and sprinkle with remaining 1/4 cup Parmesan cheese. Bake for 20 minutes more.
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