Preheat your oven broiler, and have the broiler pan handy.
In a small bowl, mix together the mayonnaise, parsley and onion. Set aside.
Put some lemon juice in one bowl and melted butter in another.
Dip the swordfish in lemon juice, then in melted butter. Place the salmon on your broiler pan and broil for 5 minutes. Turn it over and spread with the mayonnaise mixture. Sprinkle with Parmesan and continue broiling for 5 to 7 minutes, or until the fish flakes with fork and the topping is golden.
Notes
If you are preparing this recipe as gluten-free, just be sure to use a brand of mayonnaise that is known to be GF.