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 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, making sure each slice is evenly coated.
05 - Layer 3 to 4 potato slices in the bottom of each muffin cup. Spoon about a teaspoon of the cream mixture over the potatoes, then sprinkle with a pinch of cheddar and Gruyère cheese. Repeat the layers of potatoes, cream, and cheese until each 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 top with the remaining thyme leaves.
07 - Loosely cover the muffin tin with aluminum foil and bake for 30 minutes. Remove the foil and continue baking for an additional 15 minutes, until the tops are golden brown and the potatoes are 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.