Place whole baby potatoes in a large pot and cover with cold water by 1 inch. Add 1 tablespoon salt.

Bring to a rolling boil over high heat, then reduce heat slightly and boil for 15 to 18 minutes until fork-tender to the center. Drain thoroughly in a colander.

Let potatoes sit in the hot colander for 5 minutes so steam evaporates completely—dry skin is the key to shatteringly crispy edges.

Preheat oven to 425°F (220°C). Generously grease a large rimmed baking sheet with 1 tablespoon olive oil or line with parchment paper.

Space potatoes evenly on baking sheet. Use the flat bottom of a heavy drinking glass, measuring cup, or potato masher to press down gently on each potato until flattened to ½-inch thickness, keeping edges connected.

In a small bowl, stir together melted butter, olive oil, minced garlic, paprika, onion powder, oregano, thyme, and salt. Generously brush garlic butter over all potato tops, crannies, and edges.

Roast at 425°F (220°C) for 22 to 25 minutes until bottoms and ruffled edges turn deep golden and crispy.

Remove sheet from oven, sprinkle freshly grated Parmesan cheese generously over each potato, and return to oven for 8 to 10 minutes until cheese melts and forms a sizzling, bubbly golden crust.

Garnish with freshly snipped chives, fresh parsley, and flaky sea salt. Serve hot with garlic herb aioli or sour cream.