Peel the potatoes and cut them into 1/2-inch cubes. Place potatoes in a large saucepan of cold water to cover. Bring to a boil. Lower to medium heat, partially cover it, and cook for 5 minutes. It should be almost done. Drain and remove moisture with a towel. Set aside.
Melt butter in a large cast iron skillet. Once the skillet and butter are smoking hot, place potatoes in the skillet in a single layer. Let them brown without moving them for at least 30 seconds. Toss or turn the hash browns and leave them undisturbed until browned. Continue to brown on all sides, adding butter to keep potatoes from sticking.
Season with salt and pepper. Mash browned potatoes down with a plastic spatula to caramelize the bottom of the potatoes. Place a large plate on top of the skillet and invert the hash browns onto the plate. Place the remaining butter in the skillet and slide the potatoes back into the skillet, brown side up. Mash the potatoes down again and caramelize on the other side. Slide hash browns onto serving platter, or divide among plates and serve.