In a small bowl mix your butter, parsley, garlic, black pepper, sugar and lemon pee together and set aside.
Heat oil in heavy large ovenproof skillet over medium-high heat. Sprinkle the swordfish with pinch of salt and black pepper on both side.
Add swordfish to skillet and cook both sides until browned (about 3 minutes).
Place the skillet in the oven and roast for about 10 minutes or until swordfish is just cooked through.
Transfer the swordfish to plates when its ready. Add your seasoned butter to the same skillet (be careful it might be extremely hot from the oven). Cook the butter mix over medium-high heat, until the butter is melted and bubbling. Now pour the butter sauce over swordfish and serve immediately.