Preheat oven to 375°F.
Butter the baking dish thoroughly.
Slice potatoes into 1/8-inch rounds.
Layer half the potatoes in dish.
Heat cream and milk in saucepan.
Add minced garlic to cream mixture.
Season with salt and pepper.
Pour half cream over potatoes.
Sprinkle half the Gruyere cheese.
Add remaining potato layers.
Pour remaining cream mixture over top.
Cover tightly with aluminum foil.
Bake for 45 minutes covered.
Remove foil and add remaining cheeses.
Bake uncovered for 25 more minutes.
Let rest 10 minutes before serving.