Begin by cooking the spaghetti in a large pot of boiling salted water until it reaches an al dente texture, following the package instructions. Before draining, be sure to reserve some of the starchy pasta water, which will help in emulsifying the sauce later.
While the pasta cooks, place a large pan over medium heat. Once the pan is hot, add the butter and allow it to melt completely. Stir in the minced garlic and sauté for about a minute until its aroma becomes fragrant, being careful not to let it burn.
Reduce the heat to medium-low and slowly pour in the heavy cream. Stir in the freshly squeezed lemon juice, lemon zest, and parmesan, letting the cheese gradually melt into the sauce. Sprinkle in the black pepper and season with kosher salt to taste. Keep stirring until the sauce turns smooth and gently thickens.
Add the drained pasta to the pan, tossing it well to coat each strand in the velvety sauce. If the sauce needs thinning, gradually stir in a few splashes of the reserved pasta water until the desired consistency is reached.
Serve immediately, garnishing with additional grated parmesan, a sprinkle of fresh cracked black pepper, and chopped parsley if desired. Enjoy this creamy, citrus-infused pasta while warm!