Add the olive oil, capers, basil, shallots, tomatoes, lemon juice, onions, 1 1/2 teaspoons salt and 1 1/2 teaspoons pepper to a medium bowl and stir to thoroughly combine. Refrigerate until ready to use, at least 1 hour and up to overnight.
Position an oven rack at least 4 inches but no more than 6 inches from the broiler and preheat the broiler.
Place the fish fillets on a baking sheet and season with salt and pepper. Place under the broiler and cook until done on one side; watch carefully, as it may only take a couple minutes depending on the thickness of your fillets and the proximity to the broiler. Remove from the broiler and turn each fillet over. Top each fillet with about 1/2 cup of the sauce. Return to the broiler and cook until the fish is done on the other side and fully cooked through in the middle. If you are unsure about doneness, cut into the center of the fillets; the fish should be opaque (you can cover up the cut with the sauce).
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.