1/2 cup coarsely chopped parsley leaves
1/3 cup pitted Castelvetrano olives, coarsely chopped
2 tablespoons sliced chives
1 tablespoon minced shallot
2 teaspoons fresh lemon zest
1 garlic clove, minced
1/4 to 1/2 teaspoons red pepper flakes
31/2 tablespoons extra virgin olive oil, divided
Kosher salt and freshly ground black pepper
1/2 teaspoon smoked paprika
4 (6-ounce) wild Alaska salmon fillets
2 small lemons, halved
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.