Cook the pappardelle 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 a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Pour in the heavy cream and bring to a gentle simmer. Stir in the lemon zest and lemon juice, then season with salt and pepper.
Add the cooked pappardelle to the skillet, tossing to coat the pasta in the creamy lemon sauce. If the sauce is too thick, gradually add reserved pasta water until desired consistency is reached.
Stir in the grated Parmesan cheese until melted and well combined. Adjust seasoning if necessary.
Serve immediately, garnished with fresh parsley and additional Parmesan cheese if desired.