Preheat the oven: Set to 375°F (190°C) and butter a 9×13-inch baking dish.
Prep the potatoes: Peel and slice evenly (mandoline recommended for uniform thickness).
Make the béchamel sauce:
Melt butter over medium heat.
Stir in flour and cook 1 minute.
Slowly whisk in milk and cream until smooth.
Add salt, pepper, nutmeg, and garlic. Cook until slightly thickened, whisking constantly.
Layer the dish:
Spread a thin layer of béchamel on the dish bottom.
Arrange a layer of potato slices, sprinkle with cheddar and Gruyère, and drizzle more béchamel.
Repeat layers until all potatoes and sauce are used, ending with béchamel and Parmesan on top.
Bake: Cover with foil and bake 45 minutes. Remove foil and bake 20–25 minutes until golden and bubbly.
Rest: Let sit 10 minutes before serving to set layers.