Bring a pot of salted water to a boil for you pasta.
In a large skillet on medium heat, add butter until it's melted. Add the shallots and garlic, and cook for 3-4 minutes until fragrant and soft.
Add the heavy cream, lemon zest, lemon juice, and parsley, and cook for 10 minutes on medium low until sauce has thickened, stirring frequently.
While sauce is cooking, prepare your pasta until it's just al dente, reserving about ½ cup pasta water. Mix in the grated Parmesan cheese, and then add ¼ cup pasta water to the sauce along with the cooked pasta, and toss until sauce evenly coats the noodles. Add more pasta water, if needed. Sauce should be nice and creamy.
Transfer to a bowl and top with more Parmesan cheese and thinly sliced lemon peel/lemon zest, if desired
