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, 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 a teaspoon of the cream mixture over the potatoes, then sprinkle with a pinch of cheddar and Gruyère cheese. Repeat the layering process with potatoes, cream, and cheese until each muffin cup is full, pressing down gently as you build each stack.
06 - Finish 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.
08 - Remove the foil and continue baking for an additional 15 minutes, or until the tops are golden brown and the potatoes are tender when pierced with a knife.
09 - Allow the stacks to cool for 5 minutes. Run a knife around the edges of each stack to loosen, then carefully remove and serve.