Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Reserve 1/2 cup of pasta water, then drain the pasta and set aside.
In the same pot, melt the butter over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Stir in the lemon zest and juice, mixing well to combine. If the sauce is too thick, add a little reserved pasta water until you reach your desired consistency.
Add the cooked pasta to the pot and toss to coat it evenly with the lemon butter sauce. Stir in the grated Parmesan cheese, and season with salt and pepper to taste.
Serve immediately, garnished with fresh parsley and additional Parmesan if desired.