Preheat oven to 350F. Spray a 12 muffin tin with oil.
Peel potatoes, trim potatoes so they will fit into muffin tin, then slice into 1/10" thick slices. Place butter, garlic, cream, salt, pepper, and thyme in a microwave proof bowl, then melt in 30 second bursts. Stir, then set aside.
Place potato slices in the muffin pans o they go halfway up the tin. Try to match by size to make them into neat stacks. Drizzle each stack with 1/2 tsp. of cream mixture. Sprinkle half of the cheese over the stacks. Top with the remaining potato slices. Drizzle with remaining cream sauce. Cover loosely with foil and bake for 35 minutes.
Remove from oven, sprinkle with remaining cheese and bake without foil for 10 minutes or until golden and the potato is soft. Let stand for 5 minutes before removing. Use a tablespoon or butter knife to help scoop them out.