Pat dry the salmon fillets with an absorbent paper napkin.
Season both sides of the salmon with coarse sea salt and freshly cracked black pepper.
Drizzle oil in a grill pan, or grease the pan with oil spray, heat over medium-high heat.
Once the pan is hot enough, place the salmon fillets skin-side down.
Press the fish down using a spatula for a few seconds to stop it from curling. Leave it undisturbed and let it cook for 4-5 minutes. Cook on one side until the bottom of the fillet turns opaque and is cooked about 2/3rd of the way up. The skin will turn crispy and release easily from the pan. The cooking time will depend on the thickness of the salmon, mine were about 1 inch thick.
Flip and cook the other side for another 3-4 minutes. You may insert a thermometer in the thickest part of the salmon to check for doneness, the internal temperature is about 125 degrees for medium and about 145 degrees for well-done as per USDA guidelines. Remember, the salmon continues to cook after it is removed from the source of heat, so I prefer to take it off when it reaches about 140 degrees F to prevent it from drying out and overcooking.
Transfer the salmon to a platter and let it rest for 5 minutes. Arrange the salmon on a plate and top it with mango salsa. Serve with lime wedges if desired. Enjoy!