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 peeled potatoes into very thin slices, about 1/8 inch thick.
03 - In a mixing bowl, whisk together the heavy cream, milk, minced garlic, nutmeg, salt, pepper, and half of 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 the layering process until each cup is full, pressing down gently as you build.
06 - Top each stack with a final sprinkle of the remaining cheddar, Gruyère, and thyme.
07 - Cover the muffin tin loosely with aluminum foil and bake for 30 minutes. Remove the foil and continue baking for 15 minutes, or until the tops are golden brown and the potatoes are tender when pierced with a knife.
08 - Allow the stacks to cool for 5 minutes. Run a knife around the edges of each stack to loosen, then carefully remove and serve.