Heat your oven to 400 degrees. Rub the swordfish with the olive oil and season on both sides with salt and pepper. Heat a griddle pan or cast iron pan on high. Sear the fish on both sides for a couple minutes on each side. Turn off the heat and put the skillet in the oven to finish, about 10 minutes, depending on the thickness of your fish.
In a separate skillet melt butter on medium high. When the butter is hot add mushrooms, green onions, lemon juice and zest and splash of white wine. Saute for 5 - 6 minutes until mushrooms are tender and there is very little liquid left in the sauce. Season with salt and pepper to taste.
Plate the swordfish on individual plates topped with mushrooms and garnish with capers and parsley.