Heat the oil over medium-high heat in a large skillet that is already hot.
Pat the salmon pieces dry with paper towels.
Season with salt and pepper.
Once the oil is hot, carefully add the salmon pieces to the skillet, skin side down. Press down on them with a spatula when they are first added to the pan to prevent the skin from shrinking too much.
Sear the salmon for about 5 minutes, or until the skin is crispy and the fish easily releases from the pan. Carefully flip over and sear the skinless side for 1 to 2 minutes for a medium doneness.
Remove to a plate and keep warm.
Combine the basil, pine nuts, garlic and salt in a food processor and puree. With the food processor running, slowly add the olive oil and process until smooth.
Transfer the pesto to a small bowl and stir in the mayo.
Serve alongside the salmon. Optional: garnish with additional toasted pine nuts.