Cook the pasta according to package instructions until al dente. Drain and set aside.
Season the salmon fillets with salt and pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Add the salmon fillets to the skillet and cook for about 3-4 minutes per side, or until cooked through. Remove the salmon from the skillet and set aside.
In the same skillet, add the minced garlic and cook for about 1 minute, until fragrant.
Pour in the chicken broth and scrape up any browned bits from the bottom of the skillet.
Reduce the heat to medium-low and stir in the heavy cream, capers, lemon zest, and lemon juice. Simmer for 2-3 minutes, until slightly thickened.
Flake the cooked salmon into bite-sized pieces and return them to the skillet. Add the cooked pasta to the skillet and toss everything together until well coated in the creamy lemon sauce.
Remove the skillet from the heat and sprinkle chopped parsley over the pasta.
Serve the Creamy Lemon Salmon Piccata Pasta hot, optionally topped with grated Parmesan cheese.