Position an oven rack in the center of the oven and preheat the oven to 350ºF.
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 ½ 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 parchment paper-lined baking sheets.
Bake the kale until crisp and slightly dark on the edges, to 10 12 minutes. Season with the remaining ¼ teaspoon salt and 1/8 teaspoon pepper.
Let the chips cool before serving.