Cook the pasta according to package instructions in a large pot of salted boiling water. Drain and set aside, reserving 1/2 cup of pasta water.

In a large skillet, heat olive oil over medium heat. Season the salmon fillets with salt and pepper, then add them to the skillet. Cook for about 4-5 minutes on each side, or until cooked through. Remove from the skillet and flake into bite-sized pieces.

In the same skillet, add minced garlic and sauté for about 1 minute until fragrant.

Pour in the heavy cream and chicken broth, stirring to combine. Bring to a simmer and let it cook for 3-4 minutes until slightly thickened.

Stir in the lemon zest, lemon juice, and fresh spinach. Cook until the spinach wilts.

Add the cooked pasta to the skillet, tossing to coat in the sauce. If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is reached.

Stir in the grated Parmesan cheese and flaked salmon. Mix gently to combine and heat through.

Serve immediately, garnished with fresh parsley.