Preheat the oven to 500 degrees F. (Be sure your oven is very clean.) Line a sheet pan with aluminum foil.
For the Caesar sauce, place the garlic, parsley, anchovy paste, and mustard in the bowl of a food processor fitted with the steel blade and pulse until the garlic is minced. Add the mayonnaise, lemon zest, lemon juice, 1 teaspoon salt, and 1/2 teaspoon pepper and pulse to make a smooth sauce.
Place the swordfish steaks on the pan and sprinkle both sides generously with salt and pepper. Set aside one third of the sauce to serve with the cooked fish. Spread the fish on one side with half the remaining sauce, turn the fish, and spread the remaining sauce on the second side. Sprinkle with the scallions and allow to stand for 10 minutes.
Roast the fish for 10 to 12 minutes, until the center is just barely cooked. Cover the fish with aluminum foil and allow to rest on the pan for 10 minutes.
Meanwhile, heat the oil in a small saute pan until very hot, add the capers, and cook for 30 to 60 seconds, until they start to pop and are a little crisp. Serve the swordfish hot with the lemon wedges, frizzled capers, and the reserved Caesar sauce.