In a small bowl, combine panko, parsley, lemon zest, ½ teaspoon salt, and ½ teaspoon pepper. Drizzle with olive oil and stir until crumbs are evenly coated. Set aside.
Place salmon, skin side down, on a cutting board. Brush the tops of the filets with a generous amount of mustard and sprinkle with salt and pepper. Press the panko mixture thickly on each filet.
Heat vegetable oil over medium high heat in a 12 inch cast iron skillet, or other large ovenproof pan. When oil is very hot, add salmon filets, skin side down, and sear 3 to 4 minutes.
Transfer pan to hot oven and cook for 5 to 7 minutes, until salmon is almost cooked and panko is browned. Remove from the oven and cover with aluminum foil. Allow to rest for 5 to 10 minutes. Serve with lemon wedges.