Boil the potatoes:
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 and can be easily pierced with a metal or wood skewer. Make sure they are cooked through but don’t overcook. The total cooking time will be 30 to 35 minutes.
While the potatoes are cooking, set up a double layer of clean dishtowels on your countertop. As the potatoes finish cooking, 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. Repeat with all the potatoes. Don’t worry if some break apart a bit; you can still use them.1
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.
Roast the potatoes
Remove the pan of potatoes from the refrigerator, if prepared ahead. Heat the oven to 450°F. Alternatively, if you have a convection function, turn it on and set the temperature at 400°F. Sprinkle the potatoes with about 3/4 tsp. salt and pour 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, about 30 minutes if using a convection oven, 30 to 40 minutes if roasting conventionally, turning over once gently with a spatula or tongs halfway through cooking. Serve hot.
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