Bring a large pot of salted water to a boil and cook the pasta according to the package directions until al dente. Reserve 1 cup of pasta water before draining, because the starchy water helps loosen and bind the sauce.

Melt the butter in a large skillet over medium-low heat. Add the garlic and cook for about 1 minute, stirring constantly, until fragrant but not browned.

Pour in the cream and stir in the lemon zest, salt, and pepper. Simmer gently for 2 to 3 minutes, keeping the heat low so the cream stays smooth.

Add the drained pasta to the skillet and toss well. Stir in the lemon juice and Parmesan, adding reserved pasta water a few tablespoons at a time until the sauce coats every strand.

Remove the skillet from the heat and fold in the parsley. Taste and adjust the seasoning, then serve immediately with extra Parmesan, black pepper, and a little lemon zest.