Preheat oven to 350°F. Lightly grease a muffin tin with cooking spray. Peel and thinly slice potatoes (1/8-inch thick). I use a mandoline slicer for speed and accuracy (see note 1).
Add butter to a small pot over medium heat. Once melted, use a pastry brush to brush muffin tin cavities very lightly with a touch of the melted butter. Leave the rest in the pot.
Add garlic to the butter in the pot and cook for 30 seconds, stirring constantly. Stir in cream, salt (1/2 teaspoon), pepper (1/2 teaspoon), and dried thyme. Bring to a simmer, then keep warm.
Layer potato slices in the muffin tin cavities until they’re halfway full, matching sizes as much as you can. Divide cream mixture in half and drizzle one half of the cream mixture evenly over the stacks. Sprinkle with half of the grated cheese. Add remaining potato slices until stacks are about 1/4th-inch above the rim (they’ll shrink as they bake). Drizzle with the other half of the cream mixture.
Loosely cover with foil and bake for 40–45 minutes, or until a paring knife slides through the center of a stack easily.
Remove foil, sprinkle with remaining grated cheese, and bake for another 10 minutes, uncovered, or until golden and bubbly.
Remove the stacks and use a butter knife to loosen the edges. Scoop them out with a large spoon onto a plate. Grate Parmesan on top with a microplane and add fresh thyme, if desired. Serve right away.
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Notes
Note 1: Choose long, evenly sized potatoes about the width of a muffin tin cavity so the stacks bake evenly. Peel, rinse in cool water, then slice with a mandoline set to 1/8-inch thickness.Note 2: Gruyere is pricey but worth it for the flavor IMO. Sharp or extra-sharp Cheddar makes a good substitute.Note 3: Grate a little Parmesan from a block with a microplane for the perfect finishing touch.Storage: Store in an airtight container in the fridge for 3–4 days or freeze up to 2 months. Reheat in a 350°F oven until warmed through.