Preheat oven to 425°F.

Lay paper towel out on a pan or cutting board in a double layer. Place the salmon filets skin side down on the paper towel and move them around a bit to ensure the skin is bone-dry. Sprinkle the salmon filets generously with salt and pepper, then brush the upper surface with the Dijon mustard.

Place an oven safe, 10-inch or 12-inch cast-iron or stainless steel frying pan over high heat. Drizzle enough oil over the surface of the pan to coat it easily without having to swirl it, about ¼ cup. Let it stay over the high heat while you finish preparing the salmon filets.

In a pie plate or other shallow bowl, combine the pine nuts, bread crumbs, and parsley. Toss to combine evenly. Lift a salmon filet and place it, mustard down, into the mixture, pressing to help the coating adhere. Move it back to the paper towel, skin side down.

When the oil is smoking slightly, lift one filet of salmon and carefully lower it into the oil, skin side down, away from yourself. Repeat this with the other filets. Do not move the fish at all once it is in the pan. You should hear a lot of violent sizzling and there should be oil popping in the pan. This is good! Allow it to continue to sear for 4 minutes without touching or turning it. After 4 minutes, transfer the pan to the hot oven. Let the fish finish cooking in the oven, 5 to 7 minutes depending on the thickness of the filets, or until the salmon is almost cooked through and the pine nuts look toasted. Remove the pan from the oven, lightly tent with foil (being sure not to crimp the foil around the pan), and let the salmon rest for 5 minutes.

While the salmon rests, whisk together the olive oil, lemon juice, Dijon mustard, lemon zest, salt, and sugar in a mixing bowl. Add the arugula to the bowl and toss to coat evenly. Divide the arugula between 4 serving plates. Divide and scatter the pomegranate arils between the 4 salad plates. Top each salad with one filet of salmon. Garnish with additional chopped parsley, if desired, and serve immediately