Place potatoes in a large bowl, then add cheese, 1 Tablespoon of the olive oil, paprika, rosemary, garlic powder, thyme, salt, and pepper. Stir to coat potatoes evenly with the oil and spices. Add more olive oil only if needed to make the spices into enough of a paste that they adhere well to the potatoes.
1/2 cup grated Parmesan cheese, 1-2 Tablespoons olive oil, 1 teaspoon paprika, 1 teaspoon dried rosemary, 1/2 teaspoon garlic powder, 1/2 teaspoon dried thyme, 1/4 teaspoon kosher salt, 1/4 teaspoon freshly-ground black pepper