Fill a large pot with water and bring it to a boil. Add a generous amount of salt and add the pasta. While it's cooking, we'll make the sauce. Cook it for the amount of time instructed minus 2 minutes.
Preheat a large skillet to medium heat. Add the butter, oil, garlic and lemon zest and cook until slightly golden.
Add the lemon juice and let it boil down until only a bit of liquid is left.
Add the pasta water, the cream, the cooked pasta and the parmesan cheese.
Stir constantly while it cooks and thickens.
Add salt and pepper to taste and finish with fresh chives.
Serve with extra parmesan cheese, lemon zest and chives.