Bring a large pot of salted water to a boil. Add potatoes and cook until fork-tender, about 12–15 minutes. Drain well.
Mash potatoes while hot. Stir in butter, salt, pepper, garlic powder, and paprika until smooth.
Mix in 1 cup of shredded cheese until melted and creamy.
Warm tortillas briefly to make them pliable.
Spoon potato mixture into the center of each tortilla. Top with remaining cheese.
Fold in the sides and roll tightly into burritos.
Optional: Toast burritos seam-side down in a skillet over medium heat until golden and lightly crisp on both sides.
Serve warm with desired toppings.