Cook the angel hair pasta according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a large skillet, heat the 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 large pieces.
In the same skillet, add the minced garlic and sauté for about 1 minute until fragrant.
Pour in the heavy cream and bring to a gentle simmer. Stir in the Parmesan cheese, lemon juice, and lemon zest. Mix until the cheese is melted and the sauce is smooth.
Add the cooked angel hair pasta to the skillet, tossing to coat in the creamy sauce. If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is reached.
Gently fold in the flaked salmon and arugula, cooking for an additional 1-2 minutes until the arugula is wilted.
Serve immediately, garnished with fresh parsley.