Toast pine nuts in a dry small skillet over medium-low heat, tossing often, until golden and fragrant, about 3 minutes. Transfer to a cutting board. Let cool, then coarsely chop.
Heat broiler. Season flesh side of snapper fillets with salt and pepper, then sprinkle with coriander. Drizzle 2 Tbsp. oil onto a small rimmed baking sheet and place fish, flesh side down, on top. Drizzle skin side with 2 Tbsp. oil; season with salt and pepper. Broil until skin is crisp and browned and flesh is cooked through, 8–10 minutes. Remove fish from broiler and let rest 5 minutes.
Meanwhile, mix together cilantro, parsley, garlic, za’atar, red pepper flakes, and remaining ½ cup oil in a small bowl; season salsa verde with salt and pepper.
Transfer fish to a platter, placing skin side up. Stir lemon juice, banana peppers, and pine nuts into salsa verde and spoon over fish.