01 - Preheat the oven to 400°F. Grease a 12-cup muffin tin with butter or non-stick spray.
02 - Using a mandoline or sharp knife, cut the potatoes into very thin slices about 1/8 inch thick.
03 - In a mixing bowl, whisk together the heavy cream, milk, garlic, nutmeg, salt, pepper, and half the thyme until well combined.
04 - Toss the sliced potatoes in the melted butter, ensuring each slice is evenly coated.
05 - Layer 3 to 4 potato slices in the bottom of each muffin cup. Spoon a teaspoon of the cream mixture over the potatoes, then sprinkle with a pinch of cheddar and Gruyère. Repeat layers of potatoes, cream, and cheese until each cup is full, pressing down lightly as you build.
06 - Finish each stack with a final sprinkle of cheddar, Gruyère, and the remaining thyme.
07 - Cover the muffin tin loosely with aluminum foil and bake for 30 minutes. Remove the foil and continue baking for 15 more minutes, or until the tops are golden brown and the potatoes are tender when pierced with a knife.
08 - Let the stacks cool for 5 minutes. Run a knife around the edge of each stack to loosen, then carefully remove and serve.