01 - Preheat the oven to 400°F. Grease a 12-cup muffin tin generously with butter or non-stick spray.
02 - Using a mandoline slicer or a sharp knife, cut the peeled potatoes into thin, even slices about ⅛ inch thick.
03 - In a mixing bowl, whisk together the heavy cream, whole milk, minced garlic, ground nutmeg, salt, black pepper, and half of the thyme leaves until well combined.
04 - Place the sliced potatoes in a large bowl and toss with the melted butter, ensuring each slice is evenly coated.
05 - Layer 3 to 4 potato slices in the bottom of each muffin cup. Spoon about 1 teaspoon of the cream mixture over the potatoes, then sprinkle with a small pinch of both cheddar and Gruyère cheese. Repeat the layering process—potatoes, cream, cheese—until each cup is filled, pressing down gently as you build.
06 - Top each stack with a final generous sprinkle of the remaining cheddar, Gruyère, and thyme leaves.
07 - Cover the muffin tin loosely with aluminum foil and bake for 30 minutes. Remove the foil and continue baking for an additional 15 minutes, or until the tops are golden brown and the potatoes are fork-tender when pierced with a knife.
08 - Allow the stacks to cool in the tin for 5 minutes. Run a butter knife around the edges of each stack to loosen, then carefully remove and serve warm.