Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving ½ cup of the pasta water.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute, until fragrant but not browned.
Reduce the heat to low and pour in the heavy cream. Stir well to combine and let it simmer for 2-3 minutes.
Add the grated Parmesan cheese, lemon zest, and lemon juice to the skillet. Stir until the cheese is melted and the sauce is creamy. If the sauce is too thick, add a little reserved pasta water to reach your desired consistency.
Season the sauce with salt and pepper to taste. Add the cooked pasta to the skillet and toss to coat the pasta evenly with the sauce.
Serve immediately, garnished with fresh chopped parsley.