Bring a large pot of salted water to a boil and cook the pasta according to package directions until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set it aside.

While the pasta cooks, melt the butter in a large skillet over medium heat. Add the minced garlic and cook for 1 minute until fragrant.

Add the shrimp to the skillet in a single layer. Season with salt and pepper, then cook for 2 to 3 minutes per side until the shrimp turn pink and opaque. Remove the shrimp to a plate.

Pour the heavy cream into the same skillet. Add the lemon zest and lemon juice, then stir in the Parmesan cheese. Simmer for 2 minutes, adding a splash of reserved pasta water if the sauce needs thinning.

Return the cooked pasta and shrimp to the skillet. Toss everything together until the pasta is coated and heated through. Taste and adjust salt and pepper as needed.

Sprinkle with chopped parsley before serving.