Cook the Pasta - Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Reserve 1/2 cup of pasta water before draining.

Prepare the Salmon - While pasta cooks, pat salmon fillets dry with paper towels. Season both sides generously with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Cook salmon for 4-5 minutes per side until golden brown and cooked through. Remove from pan and set aside.

Make the Cream Sauce - Reduce heat to medium and add minced garlic to the same skillet. Cook for 30 seconds until fragrant. Pour in heavy cream, scraping up any browned bits from the salmon. Add Parmesan cheese and stir until melted and smooth.

Combine Everything - Flake the cooked salmon into bite-sized pieces. Add the drained pasta to the cream sauce along with salmon pieces, parsley, lemon zest, and juice. Toss everything together, adding reserved pasta water as needed to thin the sauce. Season with salt and pepper to taste.

Serve and Enjoy - Divide pasta among bowls, garnish with extra parsley and Parmesan if desired, and serve immediately.