Preheat the oven to 400 degrees F. Wash the potatoes well and place in large saucepan. Cover with cold water. Simmer over medium heat until tender, 20 minutes. Drain.
In a large skillet over medium heat, cook the chorizo in the butter until crispy. Smash the drained potatoes with a potato masher, being careful to not over-mash. Add the smashed potatoes to the skillet with the chorizo and fold until the potatoes are red and the chorizo is evenly mixed. Add in the chives. Season the potatoes with salt and white pepper. Place in a 3-quart greased baking dish. Sprinkle the cheese on top. Bake until the cheese melts, 5 to 7 minutes.