Peel potatoes, and coarsely shred them using a handheld shredder, a potato grater, or a food processor with a coarse shredding blade. Place shredded potatoes in a large bowl and add enough cool water cover them. Stir well. Drain in a colander. Repeat rinsing and draining two or three times until water runs clear. Drain again, pressing out as much water as possible with a rubber spatula.
Cook Hash Browns in Skillet
In a 10-inch nonstick skillet, heat one tablespoon of oil and butter over medium-high heat until butter foams. Add potatoes to the skillet, spreading into an even layer. Gently press with the back of a spatula to form a cake. Reduce heat to medium. Cook, without stirring, about 12 minutes or until the bottom is golden brown and crisp.
Flip and Finish Hash Browns
Invert a baking sheet or a plate over the top of the skillet. Carefully invert the skillet with the baking sheet or plate to transfer the potatoes to the baking sheet or plate. If needed, add the remaining tablespoon of oil to the skillet. Using the baking sheet or plate, slide the potatoes back into the skillet, uncooked side down. Cook, without stirring, about 8 minutes more or until the bottom is golden brown. If desired, sprinkle with paprika before serving.