Cook the pasta in salted water until al dente, then drain and set aside.
Pat the salmon dry and season with salt, pepper, and garlic powder.
Dredge the salmon lightly in flour on all sides.
Heat olive oil and butter in a skillet over medium-high heat.
Cook the salmon for about 3 minutes per side until golden brown, then remove and set aside.
Pour out any excess fat from the pan, leaving the browned bits.
Add chicken broth and pesto, scraping the bottom to deglaze the pan; cook for 30 seconds.
Stir in heavy cream and lemon juice; simmer the sauce for 1 minute.
Return the salmon to the pan, breaking it into bite-sized chunks.
Simmer the sauce for 3–5 minutes until thickened and salmon is fully cooked.
Add the cooked pasta to the sauce and toss gently to combine.
Serve immediately with freshly grated Parmesan cheese, if desired.