Preheat oven to 425°. Pat fish dry with paper towels, and let stand at room temperature for 10 minutes. Sprinkle filets with salt and pepper.
Heat oil in a large ovenproof skillet over medium-high heat. Ensure pan is hot before adding fish. Carefully place filets, top side down, in hot oil. Press very lightly with a spatula while cooking for even searing. Cook 3 to 4 minutes or until the edges are lightly browned.
Transfer skillet to oven. Bake at 425° for 4 to 5 minutes or until the 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, shallot, and lemon juice. Season with salt and pepper, as needed. Serve on top of grouper filets.