Position an oven rack in the center of the oven, and preheat the oven to 350°F.
Using a mandoline slicer or a sharp knife, slice the potato into 1/8-inch-thick slices. Put in a bowl, and drizzle with 1 tablespoon of the olive oil. Toss well. Arrange in a single layer (without overlapping) on parchment-lined baking sheets.
Bake for 12 minutes. Turn the slices over, and continue to bake, checking every 2 minutes, until brown and crisp, 6 to 8 minutes longer. Season the chips with 1/2 teaspoon of the salt and 1/8 teaspoon of the pepper.
Remove the thick stem from the kale leaves, and discard. Cut the leaves into 2- to 3-inch pieces. Put in a bowl, and drizzle with the remaining 1 tablespoon olive oil. Toss well. Arrange the kale in a single layer on a parchment-lined baking sheets.
Bake the kale until crisp and slightly dark on the edges, 10 to 12 minutes. Season with the remaining 1/4 teaspoon salt and 1/8 teaspoon pepper.