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, whole milk, minced garlic, ground nutmeg, salt, black pepper, and half of the thyme leaves until well combined.
04 - Toss the thinly sliced potatoes in the melted butter, ensuring each slice is evenly coated.
05 - Layer 3 to 4 potato slices in the bottom of each greased muffin cup. Spoon a teaspoon of the cream mixture over the potatoes, then sprinkle with a pinch of cheddar and Gruyère cheese. Repeat the layers—potatoes, cream, cheese—until each muffin cup is full, pressing down gently as you build each stack.
06 - Finish each stack with a generous sprinkle of the remaining cheddar and Gruyère cheese and 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 easily pierced with a sharp knife.
08 - Allow the stacks to cool in the tin for 5 minutes. Run a butter knife around the edge of each stack to loosen, then carefully remove and serve warm.