Preheat oven to 400 degrees F (200 degrees C). Spray a 9×13-inch baking pan or cast iron skillet with cooking spray; pour in about 1 teaspoon vegetable oil to coat the bottom.
Mix Parmesan cheese, salt, garlic powder, paprika, and black pepper together in a bowl.
Blot the cut-side of potatoes with a paper towel to remove any moisture. Place potatoes in a bowl and drizzle with 1 tablespoon vegetable oil; toss until potatoes are lightly coated. Sprinkle potatoes with Parmesan cheese mixture; toss to coat. Arrange potatoes, cut-side down, onto the prepared baking pan.
Bake in the preheated oven for 15 to 20 minutes. Turn potatoes to cut-side up; continue baking until golden and crispy, about 15 to 20 more minutes. Serve with sour cream.
It is important that you get as much of the Parmesan mixture as possible onto the cut side of the potatoes. As I place the potatoes into the baking pan, I press the cut sides directly onto the Parmesan mixture that sticks to the sides and bottom of the bowl, distributing it as evenly as possible among the potatoes.
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