Preheat oven to 350°F and butter a 9x13-inch baking dish.
Slice potatoes uniformly and soak in cold water.
Melt butter in saucepan, sauté garlic until fragrant.
Add flour to form a roux, then whisk in cream and milk slowly.
Season with salt, pepper, nutmeg, and thyme; simmer until thick.
Stir in cheddar and Gruyere until melted.
Layer potatoes, sauce, and cheese in dish; repeat three times.
Cover with foil and bake for 60 minutes.
Remove foil, top with Parmesan and breadcrumbs, bake 25 more minutes.
Rest 10–15 minutes before serving.