Preheat the oven to 450 degrees F.
Leaving peel on, cut the potatoes into 6 lengthwise to make long wedges, about 3/4-inch to 1-inch wide. Combine the potatoes, oil, salt and cayenne on the baking sheet and toss to combine. (1 less bowl to wash) Arrange the potatoes on a baking sheet in a single layer, so a cut side is in contact with the pan, but evenly spaced so the potatoes aren't touching each other. Bake until golden brown and cooked through, about 30 minutes. Slip a spatula under the potatoes to turn them over and cook for 5 minutes more.
Transfer potatoes to a serving dish and serve immediately.