Peel the potatoes and cut them into quarters. Place them in a large pot and fill it with water until the potatoes are submerged.
Bring the pot of water to a boil over high heat. Once boiling, reduce the heat to medium and simmer the potatoes for about 15-20 minutes, or until they are fork-tender.
Drain the cooked potatoes and transfer them to a mixing bowl. Use a potato masher or ricer to mash the potatoes until smooth.
Add the flour, egg, salt, black pepper, garlic powder, and paprika to the mashed potatoes. Mix until all the ingredients are well combined and a dough forms.
Preheat your oven to 425°F (220°C) and line a baking sheet with parchment paper.
With lightly floured hands, take a portion of the potato mixture and shape it into a fry shape, about 1/2 inch thick. Place the formed fries onto the prepared baking sheet.
Drizzle the vegetable oil over the fries, ensuring they are evenly coated. Use a spoon or spatula to flip the fries, making sure they are covered in oil on both sides.
Bake in the preheated oven for 20-25 minutes, flipping the fries halfway through, until they are golden brown and crispy.