Peel the potatoes and cut into 1/3-inch dice. Melt the butter in a large skillet over medium heat and add the onion. Cook, stirring often, until softened, about 5 minutes. Season with salt and pepper. Use a slotted spoon to transfer the onion to a small bowl. Add the vegetable oil to the skillet and heat until almost smoking. Add the potatoes and leave to form a crisp crust. Do not disturb the potatoes until the crust is formed, about 5 minutes. Check to see if a crust has formed; if so, give a quick stir. If not, continue cooking for another 1 to 2 minutes, until the crust has formed. With a spatula, turn over large chunks of the crusted potatoes. Season with salt and pepper and continue cooking until golden brown. Stir in the onion, season again with salt and pepper, and stir until the hash is heated through, about 3 minutes.