Peel potatoes and cut into small cubes of equal sizes (1/2 inch or less). Place in a pot, cover with about 2 inches of water, add salt, and cook on medium-high heat for 5 minutes, or until just tender enough to be easily pricked with a fork, but not so soft they crumble. Drain well in a colander.
Transfer potatoes to a rimmed baking sheet, drizzle with 4 tablespoons of the oil, and toss with your hands until all of the potatoes are coated. (Use remaining oil, if necessary). Spread potatoes evenly over baking sheet, and sprinkle with salt.
Bake at 425F for 30 minutes, turning them with a spatula every 10 minutes. (Watch after 15 minutes of cooking, and remove them if they are golden brown all over and soft when pierced with a fork, if not continue baking). Serve hot.