Preheat oven to 375°F.
Butter the baking dish generously.
Slice potatoes very thinly using mandoline.
Heat cream and milk in saucepan.
Add garlic and bay leaf.
Simmer mixture for 5 minutes.
Remove bay leaf from cream.
Layer half the potatoes in dish.
Season with salt and pepper.
Pour half the cream mixture over.
Add remaining potato layers carefully.
Pour remaining cream on top.
Cover tightly with aluminum foil.
Bake covered for 30 minutes.
Remove foil and add cheeses.
Bake uncovered for 15 minutes.
Rest for 10 minutes before serving.