Preheat oven to 350°F.
In a small saucepan, melt the butter over medium-low heat. Generously brush 12 muffin tin cups with butter.
Place one sprig of thyme at the bottom of each muffin cup and set aside.
Add the chopped thyme and garlic to the butter to the saucepan and heat a couple of minutes until fragrant, remove from heat and set aside.
Using a mandolin, slice the creamer potatoes into very thin rounds approximately 1/16 inch thick.
Place in a medium bowl and pour the herb butter over the sliced potatoes.
Add the kosher salt and pepper to the bowl and stir with a wooden spoon until well coated.
Start to layer the little potato slices into each of the muffin cups overlapping the thin slices in a circular pattern. Make sure the slices are divided equally between the cups. Press down gently on each cup after it is filled.
Cover the muffin tin tightly with foil and place on a cookie sheet.
Bake in your preheated 350°F oven for 35 minutes or until the potatoes can easily be pierced with a fork. Remove the foil.
Prepare a parchment-lined baking sheet. Lay the parchment paper over the muffin tin. Place the new baking sheet over the muffin tin and flip over. The little potatoes should come right out onto the parchment-lined baking sheet. If any of them stick, use a fork to carefully remove them and re-stack them.
(If making ahead, stop here. Allow the potato stacks to cool, cover with plastic wrap and refrigerate. They will keep for up to 24 hours. Proceed with the rest of the recipe when ready. Try to allow the potatoes to come up to room temperature and remove the plastic wrap before baking. You will have to add at least 5 to 10 minutes of baking time to each side to get them crispy as the potatoes will be cold.)
Increase the oven temperature to 425°F.
Place into the preheated oven and bake for 10 minutes or so until the bottom is golden and crispy. Remove from the oven and carefully turn each potato stack using a small spatula so that the thyme sprig side is down.
Bake for an additional 10 minutes or until the bottom again is golden and crispy and the potatoes are tender.
Serve thyme sprig side up immediately.
