Cook the pasta according to package instructions until al dente. Drain and set aside.
Preheat the oven to 400°F (200°C). Season the salmon fillets with salt and pepper and brush them with olive oil. Place salmon filets on the baking sheet lined with baking paper. Bake them in the oven for 10 minutes or until cooked through and flaky. Remove the salmon from the oven and set aside.
Prepare the pesto sauce. In a food processor or blender, combine the basil leaves, grated Parmesan cheese, pine nuts (or walnuts), minced garlic, salt, and pepper. Pulse several times until the ingredients are roughly chopped. Drizzle in the extra-virgin olive oil until the mixture is smooth and well combined. Adjust the salt and pepper to taste.
In the same skillet, where the salmon was cooked, add the cooked pasta and pesto sauce. Toss well to coat the pasta evenly with the pesto.
Flake the cooked salmon into bite-sized pieces and add it to the skillet. Gently mix everything together until the salmon is well incorporated into the pasta. Cook for an additional 1-2 minutes, stirring gently, to warm up the salmon and ensure all the flavors are combined. Remove from heat and serve the salmon pesto pasta hot. Garnish with grated Parmesan cheese, halved cherry tomatoes, or fresh basil leaves for extra flavor and visual appeal!