Cook pasta according to package directions, drain water out and transfer the pasta into a large salad bowl and allow the pasta to cool down completely.
Season salmon:
Pat dry salmon fillets with a paper towel and season with salt and pepper on both sides.
Cook salmon:
In a large skillet, heat oil and butter over medium-high heat. Add the salmon to the pan and cook for 3 to 4 minutes per side until golden/seared on each side and the meat separates easily with a fork. Remove from the pan onto a plate.
Combine:
Break up the salmon into large pieces and add them to the pasta bowl along with the red onions and cherry tomatoes.
Add the pesto into the salad bowl, the lemon juice, and toss to combine all ingredients to evenly distribute the pesto throughout. If it's too thick, add a tablespoon or two of water to stretch the dressing a little.
Sprinkle parmesan cheese and fresh basil shreds, if using, and toss to combine before serving.