Cook potatoes in boiling, salted water until soft. Drain and set aside.
In a non-stick, oven-safe pan, render chorizo until slightly brown. Fold in potatoes and gently smash them with a rubber spatula. Add butter, chives, salt and pepper. Mix well.
Sprinkle potatoes with cheese and immediately place in the oven.
Broil for 30 to 45 seconds to brown cheese. Serve immediately.