In a medium-size bowl whisk together the panko bread crumbs, lemon zest, 1/2 teaspoon salt, 1/2 teaspoon pepper, and parsley. Drizzle the olive oil over the top and mix to coat the breadcrumb mixture. Set aside.
Rinse the salmon fillets and pat them dry with paper toweling; place them on a platter skin side down. Using a pastry brush, generously brush the salmon with the Dijon mustard. Top the salmon with the panko mixture, gently pressing it into the mustard to help secure the coating.
Add the vegetable oil to a large ovenproof skillet. (Cast iron is great for this) heat the oil over medium-high heat until very hot. Place the salmon in the skillet skin side down and cook until skin is crispy.
Move the skillet to the oven to finish cooking the fish. Bake until fish flakes easily with a fork and bread crumbs are browned. (I used an instant-read thermometer to an internal temperature of 145F.) About 10 minutes.