Preheat the oven to 350° F. Line a baking sheet with parchment paper.
Make the pesto. Combine the basil, garlic, and nuts in a food processor. While the food processor is running, add the olive oil slowly and steadily until the mixture is emulsified. Season with salt and pepper.
Roughly chop the spinach.
Stir the pesto, spinach, and breadcrumbs together in order to form the topping for the salmon. Season the mixture with more salt and pepper as desired.
Coat each piece of salmon with the pesto crumb topping, dividing the mixture equally between the filets.
Spray the coated salmon pieces with olive oil spray, place them evenly onto your baking sheet, and place into the preheated oven.
Bake the salmon at 350° F for 15-20 minutes, depending on the thickness of the fish. You want for the topping to brown slightly and for the fish to cook through.