Cut the potatoes into small cubes and soak in cold water until ready to use to prevent browning.
Preheat the oven to 400ºF. Line a large sheet pan with parchment paper and set aside.
In a small bowl, add the garlic, cornstarch, salt, thyme, oregano, black pepper, and Parmesan cheese. Pour over the oil and stir to combine.
Drain and completely dry the potatoes. Add the seasoning mixture to the potatoes and toss to coat.
Spread the potatoes out around the sheet pan so they are in a single layer. Make sure to leave space so the potatoes can crisp– if your baking sheet is too crowded, roast the potatoes on two separate sheets instead.
Bake until golden and crisp, about 50 minutes, flipping halfway through. Immediately after removing the potatoes from the oven, add the butter, fresh parsley, and extra salt, to taste, to the pan. Toss until the butter melts onto the potatoes and the parsley is evenly distributed. Serve warm.