Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente. Reserve 1/2 cup of pasta water before draining.
Season salmon fillets on both sides with salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Sear salmon for approximately 4 minutes per side until cooked through. Remove from pan and flake into large bite-sized chunks.
Wipe the skillet and melt butter over medium heat. Add the shallot and garlic, sautéing for 2 minutes until translucent and fragrant.
Whisk in the heavy cream, lemon juice, and lemon zest. Simmer for 2 to 3 minutes until the sauce begins to thicken slightly.
Add the cooked pasta and the flaked salmon to the skillet.
Toss gently to combine, adding the reserved pasta water 1 tablespoon at a time if the sauce is too thick.
Stir in the fresh parsley and serve immediately.