01 - Preheat 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 about 1/8-inch thick. Uniform slices ensure 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 - Place the sliced potatoes in a large bowl and toss with the melted butter, ensuring each slice is evenly coated for golden browning during baking.
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 small pinch of both 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 cheeses and the reserved thyme leaves for a golden, flavorful crust.
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, or until the tops are deep golden brown and the potatoes are fork-tender when pierced with a sharp knife.
08 - Allow the stacks to rest for 5 minutes in the tin. Run a small knife around the edges of each stack to loosen, then gently lift out and serve warm.