Step 1

Preheat oven to 325°F with rack in middle position. Whisk together 1/2 cup oil and paprika in a small bowl. Set aside 1 tablespoon oil mixture; stir lemon zest and juice into remaining oil mixture in small bowl. Place salmon in a large baking dish; sprinkle both sides with 21/2 teaspoons salt and 1/2 teaspoon pepper. Tuck tapered end of salmon under if needed to fit in dish. Pour lemon-paprika mixture over salmon. Bake in preheated oven until thickest part of salmon flakes easily with a fork, 30 to 35 minutes, spooning lemon-paprika mixture in baking dish over salmon every 10 minutes. Remove from oven; let rest 5 minutes.

Step 2

Whisk together parsley, walnuts, vinegar, olives, and remaining 1/4 cup oil in a small bowl. Season with remaining 1/4 teaspoon salt and remaining 1/4 teaspoon pepper. Using 2 large spatulas, carefully lift salmon from baking dish, and transfer to a large platter; discard remaining lemon-paprika mixture in baking dish. Spoon walnut-olive vinaigrette on salmon. Drizzle fish with reserved oil mixture. Serve warm or at room temperature.