In a small bowl, mix together the panko, parsley, lemon zest, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Drizzle with the olive oil and stir until the crumbs are evenly coated. Set aside.
Place the salmon fillets, skin side down, on a board. Generously brush the top of the fillets with mustard and then sprinkle generously with salt and pepper. Press the panko mixture thickly on top of the mustard on each salmon fillet. The mustard will help the panko adhere.
Heat the vegetable oil over medium-high heat in a 12-inch cast-iron skillet or large heavy, ovenproof pan. When the oil is very hot, add the salmon fillets, skin side down, and sear for 3 to 4 minutes, without turning, to brown the skin.
Transfer the pan to the hot oven for 5 to 7 minutes until the salmon is almost cooked and the panko is browned. Remove from the oven, cover with aluminum foil, and allow to rest for 5 to 10 minutes. Serve the salmon hot or at room temperature with lemon wedges.
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