Preheat your oven to 425°F (220°C). Line a baking sheet with parchment paper.
Wash and peel the potatoes, then cut them into thin fries (about 1/4 inch thick).
In a large bowl, toss the potato fries with olive oil, paprika, garlic powder, onion powder, cayenne pepper, oregano, salt, and black pepper until evenly coated.
Spread the seasoned fries in a single layer on the prepared baking sheet. Bake for 25-30 minutes, flipping halfway through, until they are golden brown and crispy.
Remove the fries from the oven and sprinkle the shredded cheddar cheese on top. Return to the oven for an additional 5 minutes, or until the cheese is melted.
Once out of the oven, top with sliced green onions and serve with sour cream on the side, if desired.