The robust salsa is a dominant presence on the plate. Sweet and mellow roasted fennel makes a particularly fitting side.
Combine 1 tablespoon oil, 1/8 teaspoon pepper, parsley, and next 6 ingredients (through anchovy paste) in a small bowl, tossing well; set aside.
Heat a large nonstick skillet over medium-high heat. Add remaining 1 teaspoon oil to pan; swirl to coat. Sprinkle fish fillets evenly with salt and remaining 1/8 teaspoon black pepper. Add fish fillets to pan; cook 4 minutes on each side or until desired degree of doneness. Serve fish with salsa verde.