Slice the shallots and leeks and fry them in olive oil and butter until softened, about 7-10 minutes.
Follow with the garlic for another minute.
Meanwhile, mix egg and Parmesan with a bit of pasta water and then pour the drained pasta into the leek pan, remove from the heat and slowly dribble in the egg mix stirring constantly.
Continue stirring until you have a silky sauce, season and serve with more parmesan.
