Bring the salmon to room temperature 20 minutes before grilling.
Preheat the oven to 450 degrees F. Set a large cast-iron grill pan over low heat and pre-heat for 1 minute.
Meanwhile, brush the salmon lightly with the oil and season with salt and pepper.
Raise the heat under the grill pan to medium-high. Place the salmon, skin-side up on the grill, at an angle across the ridges of the pan. Cook until the fish has distinctive grill marks, about 3 minutes. To make cross-hatched grill marks, use a spatula to re-position the fillets about 45 degrees (keep the skin-side up). Cook 2 minutes more. Turn the salmon over, and transfer the grill pan to the oven. Continue cooking the fish in the oven for 2 to 3 minutes for pink inside, 5 minutes for medium, and 7 minutes for well done.
Remove the fish from the pan, and let rest for 2 minutes, to finish cooking. (If the skin comes loose during cooking, you may remove and discard it before serving, if desired.) Serve.
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