12 to 15 baby red or yellow potatoes
2-3/4 tsp. kosher salt
1/2 cup extra-virgin olive oil
Put the potatoes in a large saucepan (preferably in one layer) and cover with at least an inch of water. Add 2 tsp. kosher salt to the water. Bring the water to a boil over high heat, reduce to a simmer, and cook the potatoes until they are completely tender, 30 to 35 minutes.
While the potatoes are cooking, set up a double layer of clean dishtowels on your countertop. When the potatoes are done, remove them individually from the water, and let them drain and sit for just a minute or two on the dishtowels.
Fold another dishtowel into quarters, and using it as a cover, gently press down on one potato with the palm of your hand to flatten it to a thickness of about 1/2 inch. Cover a large rimmed baking sheet with aluminum foil; put a sheet of parchment on top of the foil. Transfer the flattened potatoes carefully to the baking sheet and let them cool completely at room temperature.
Heat the oven to 450°F. Sprinkle the potatoes with about 3/4 tsp. salt and drizzle the olive oil over them. Lift the potatoes gently to make sure some of the oil goes underneath them and that they are well coated on both sides. Roast the potatoes until they’re crispy and deep brown around the edges, 30 to 40 minutes. Turn over once gently halfway through cooking. Serve hot.