Bring the stock to a simmer in a pot on the stove. Add the carrot, pasta and meatballs and simmer for about 10 minutes, until the meatballs are cooked through and the pasta is tender.
In a small bowl, whisk together the egg and Parmesan cheese; drizzle into the hot soup, stirring gently so that it doesn't completely blend in, but cooks in strands. Throw in the spinach and cook for another minute or two, until it wilts.
Season with salt and pepper, and serve with extra Parmesan cheese on top.