Saute celery, onion, carrot, garlic, and ham until veggies are soft and the mixture is lightly browned, about 15 minutes.
Add wine, scraping up any browned pieces. This is a big part of the delicious flavor of this dish, so don't rush.
Continue cooking until liquid is almost evaporated.
Add broth, Italian herbs, and the baby leaf. Bring mixture to a boil, and then simmer for 30 minutes.
Drop meatballs into simmering soup and cook for about 5 minutes, until meatballs float.
Add beans and parsley. Remove bay leaf.
Whisk eggs. Add about 1 cup of the broth to eggs, continuing to whisk lightly.
Remove the pot from heat, stirring in the egg mixture.
Top soup with Parmesan cheese.