Look for fillets displayed on ice rather than in packages. They should smell like the ocean, not overly fishy.
Heat broiler, with rack in top position. Lightly coat a rimmed baking sheet with cooking spray. Fold fish into thirds and place in center of sheet, seam side down; season with salt and pepper. Toss artichoke hearts with anchovy and scatter around fish. Broil until fish is opaque throughout, 3 to 6 minutes. Transfer fish to a plate. Toss artichoke mixture with marinade and lettuce and serve alongside fish.