Preheat the oven to 425°F (220°C) if baking the fries or heat the oil in a fryer.
Wash and cut the potatoes into thin fries. Soak them in cold water for about 10 minutes to remove excess starch, then drain and pat dry.
In a large bowl, toss the fries with vegetable oil, paprika, garlic powder, onion powder, chili powder, and salt until they are evenly coated.
If baking, spread the fries in a single layer on a baking sheet. Bake for 20-25 minutes, flipping halfway through, until they are golden brown and crispy. If frying, cook the fries in hot oil until golden brown, about 5-7 minutes.
While the fries are cooking, prepare the cheese sauce. In a saucepan, melt the butter over medium heat. Whisk in the flour and cook for 1-2 minutes until bubbling, forming a roux.
Slowly add the milk while whisking continuously until smooth. Bring to a gentle simmer, then stir in the cheddar cheese until melted and creamy. Add cayenne pepper and salt to taste.
Once the fries are cooked, remove them from the oven or fryer and place them on a serving platter.
Drizzle the cheese sauce over the fries before serving.