01 - Preheat the oven to 400°F. Generously grease a 12-cup muffin tin with butter or non-stick cooking spray.
02 - Using a mandoline slicer or a sharp knife, cut the peeled potatoes into thin, even slices approximately 1/8 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 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 approximately 1 teaspoon of the cream mixture over the potatoes, then sprinkle with a pinch of cheddar and Gruyère cheese. Repeat the layering process — potatoes, cream, cheese — until each cup is filled, pressing down gently between layers.
06 - Finish each stack with a generous sprinkle of the remaining cheddar and Gruyère cheese, along with the reserved 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 small knife around the edges of each stack to loosen, then carefully remove and serve warm.