• Preheat oven to 350°F. Use the butter to coat the inside of a 13x9-inch baking dish. Set aside.
• In a saucepan, combine heavy cream, shallots, garlic, salt and pepper, and thyme. Bring to a gentle simmer and cook until shallot and garlic are softened, about 15 minutes. Transfer to a blender or stick blend until smooth. If using a traditional blender, be VERY careful as the mixture will be hot.
• While the cream mixture is cooking, slice potatoes using a mandolin to ⅛-inch thickness and  transfer a bowl of water to get rid of excess starch and prevent browning. After all potatoes are sliced, drain sliced potatoes well.
• Take the sliced potatoes and shingle them across the bottom of the baking dish, filling in any gaps with smaller pieces of potato. Pour the blended cream mixture evenly over the potatoes.
• Cover with foil and bake for 50-60 minutes or until the potatoes are fork tender. Remove foil, top with grated cheeses and return to oven with oven rack closest to the broiler and  broil for 5-10 minutes until the cheese is super melty and golden brown.

To prep ahead of time:

• The day before, assemble the dish and bake, covered with foil, for 50-60 minutes. Allow to cool and refrigerate overnight. When ready to serve, reheat in a 350°F oven, covered with foil, for 20 minutes or until hot, uncover, top with the cheeses and broil for 5-10 minutes.