Preheat oven to 400 degrees F (200 degrees C). Spray a 9x13-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.