Cook the pasta according to package instructions. Reserve 1/2 cup pasta water, drain, and set aside.
Season the salmon with salt and pepper.
In a skillet, heat olive oil and cook the salmon until lightly golden and cooked through. Remove and flake into chunks.
In the same skillet, melt butter and sauté garlic.
Add chicken broth, lemon zest, and lemon juice.
Stir in the heavy cream and Parmesan, letting the sauce thicken.
Add spinach and let it wilt.
Add the salmon back into the sauce.
Toss the pasta with the sauce, adding pasta water as needed for consistency.
Serve with fresh parsley and additional Parmesan.