Preheat oven to 425°F.
Pat fish dry with paper towels, and let stand at room temperature 10 minutes. Season with salt and pepper.
Heat oil in a large ovenproof skillet over medium-high heat. Carefully place fish in hot oil. Cook 3 to 4 minutes or until the edges are lightly browned.
Transfer skillet to oven. Bake at 425°F for 4 to 5 minutes or until fish is opaque. Remove skillet from oven, and place fish, seared side up, on a platter. Wipe skillet clean.
Cook butter in skillet over medium heat 2 to 2 1/2 minutes or until butter begins to turn golden brown.
Pour butter into a small bowl. Whisk in vinegar, green onion, and lemon juice. Season with salt and pepper.
Brush fish with the butter mixture and garnish with fresh parsley.