Lightly grease a 12-cup muffin pan with a little extra virgin olive oil. Sprinkle a dash of salt in the bottom of each cup, as well.
In a small bowl, mix together 1/4 cup parmesan cheese, thyme leaves, salt, black pepper, and garlic. Set aside.
Thinly slice each potato to be 1/8" - 1/16" thick (a mandoline is easiest to use to achieve the 1/16" thickness).
In each cup, add 4-5 sliced potatoes, then brush with the oil mixture, then continue stacking until each cup is filled to the top with potato slices. Add any remaining oil mixture on the top of the potato stacks, as well as the remaining 1/4 cup parmesan.
Bake the potatoes for 35-45 minutes, until your desired crispiness. Sprinkle with flaky sea salt and serve warm. Enjoy!