Preheat the oven to 425°F (220°C) if baking, or heat oil in a deep fryer or large pot to 350°F (175°C).
Wash and peel the russet potatoes, then cut them into thin fries, about ¼ inch thick.
In a mixing bowl, toss the cut fries with olive oil, paprika, garlic powder, onion powder, chili powder, salt, and black pepper until evenly coated.
If baking: Place the seasoned fries in a single layer on a large baking sheet and bake for 25-30 minutes, flipping halfway through, until crispy. If frying: Carefully add the fries to the hot oil in batches, cooking for about 4-5 minutes until golden brown and crispy. Remove and drain on paper towels.
While the fries are cooking, make the cheese sauce. In a saucepan over medium heat, melt the butter, then add the flour and whisk for about 1 minute to create a roux.
Gradually whisk in the milk, stirring constantly until the mixture thickens.
Remove the saucepan from heat and stir in the shredded cheddar cheese, paprika, cayenne pepper (if using), and salt until the cheese is melted and the sauce is smooth.
Serve the hot fries drizzled with the cheese sauce, and enjoy!