Finely chop the parsley with the stalk; whisk with the egg and a dash of cooking water. Finely grate the parmesan and stir in most of it.
Pour the drained tagliatelle into the hot pan with the meatballs, pour in the whisked egg and toss for 1 minute. Dilute everything with a good dash of cooking water. Season everything with salt and pepper and sprinkle with the rest of the parmesan before serving.