Preheat oven to 425°. In a large pot, cover potatoes with water and add a generous pinch of salt. Bring water to a boil and simmer until potatoes are tender, about 15 minutes. Drain and let sit until cool enough to handle.
On a large baking sheet, toss potatoes with garlic, butter, and thyme. Using the bottom of a small glass or mason jar, press down on potatoes to smash them into flat patties; season with salt and pepper. Sprinkle with Parmesan.
Bake potatoes until bottoms are beginning to crisp and Parmesan is golden, about 25 minutes.
