Stir together parsley, olives, chives, shallot, zest, garlic, and red pepper flakes. Drizzle with 2 tablespoons olive oil tossing to coat. Season with salt and pepper to taste.
Combine paprika, 1 teaspoon salt, and 1/2 teaspoon pepper. Sprinkle and rub paprika mixture onto filets.
Heat a large heavy skillet over medium heat until hot; add remaining 11/2 tablespoons oil swirling to coat. Add fillets skin side up and cook until golden brown, about 4 minutes. Turn fillets over and cook until golden and just cooked through, about 3 to 4 minutes. Remove and let stand a few minutes. Cook lemon halves cut side down until charred, about 2 to 3 minutes.
Arrange fillets on a serving dish. Spoon salsa verde on top of filets. Serve warm with charred lemons.
Ingredients
1/3 cup Castelvetrano olives, pitted, coarsely chopped
