How to Make It
Rinse garlic scapes, and pat dry with paper towels. Trim and discard woody ends and curly tops. Cut scapes into 1/8-inch-thick slices to equal 1/3 cup. (If using scallions and garlic, slice scallions to equal 1/3 cup, and thinly slice garlic to equal 1 teaspoon.) Combine garlic scapes, olive oil, lemon juice, 1 tablespoon water, dried oregano, red pepper, and bay leaf in a small saucepan. Season with salt and pepper. Bring to a simmer over medium. Reduce heat to low; cook, stirring often, until mixture is softened and darkened, about 5 minutes. Remove from heat; let cool 20 minutes. Discard bay leaf; stir in lemon zest.
Cut 2 shallow diagonal slashes across skin of each fillet; arrange in a single layer on a rimmed baking sheet lined with parchment paper. Brush both sides of fillets with 3 tablespoons garlic scape oil, and season with salt to taste. Stir tomato and fresh oregano into remaining oil; set salmoriglio aside.
Preheat oven to 450°F. Heat a large ovenproof skillet over medium-high until very hot, about 4 minutes. Add vegetable oil; heat until very hot, about 1 minute. Add fillets, skin sides down. Press fillets gently with a spatula. Reduce heat to medium, and cook until skin begins to brown around edges, about 4 minutes. Transfer skillet to preheated oven, and roast until fish is opaque and just cooked through, about 4 minutes. Flip fillets, and divide among 4 plates, skin sides up. Spoon salmoriglio evenly over each fillet. Sprinkle servings with arugula and parsley.