01 - Preheat the oven to 400°F. Grease a 12-cup muffin tin generously with butter or non-stick cooking spray.
02 - Using a mandoline slicer or a sharp knife, cut the peeled potatoes into thin, even slices about ⅛ inch thick. Uniform thickness ensures even cooking throughout each stack.
03 - In a mixing bowl, whisk together the heavy cream, whole milk, minced garlic, ground nutmeg, salt, pepper, and half of the thyme leaves until well combined.
04 - Toss the sliced potatoes in the melted butter, making sure each slice is evenly coated to promote browning and prevent sticking.
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 cheese. Repeat the layering process — potatoes, cream, cheese — until each muffin cup is filled to the top, gently pressing down as you build each layer.
06 - Finish each stack with a generous sprinkle of the remaining cheddar and Gruyère cheese, then top with the remaining thyme leaves.
07 - Cover the muffin tin loosely with aluminum foil and bake for 30 minutes to allow the potatoes to steam and soften in the cream mixture.
08 - 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.
09 - 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.