Preheat oven to 375°F/190°C. Lightly brush the cups of a 12-cup muffin tin with oil.
Melt butter and stir in garlic, parsley, chopped thyme, salt and black pepper. Set aside to cool.
Slice potatoes with skin on, very thinly about 1/16”.
Place sliced potatoes in a large mixing bowl and toss with cooled garlic herb butter.
In each oiled muffin cup, place a small sprig of thyme, followed by slices of potatoes starting with smaller pieces and ending with the larger pieces, sprinkling a bit of grated parmesan between layers.
Cover muffin tin tightly with foil. Bake in preheated 375°F/190°C oven for 25 minutes or until potatoes are tender.
Increase oven heat to 425°F/220°C. Remove foil and return to bake uncovered for 13-15 minutes more, or until edges are browned and crispy.
Use a wooden skewer to dislodge the stacks from the muffin tin and serve upside down with a sprinkle of flaky salt.
Tags: egg-free, eggless, gluten-free, holiday, nut-free, potato, side, vegetarian
