Combine meat, salt, pepper, garlic, parsley, egg and breadcrumbs in a bowl, adding more breadcrumbs as needed until the meat is workable. Form meat mixture into golf-ball sized balls, placing a cube of mortadella in the middle of each.
In a deep-set pan, simmer milk over low heat. Place the balls in the simmering milk to braise.
Add olive oil, celery and shallot to a large pot, cook until softened. Add chicken stock and if more liquid is needed, add water.
After the meatballs are simmered and the milk has formed some curds, use a slotted spoon to transfer the meatballs from the milk to the broth mixture.
Stir in spinach. Add pasta and let cook for 60 seconds.
In a bowl, beat eggs and add to broth. Stir. Grate nutmeg directly into broth, to taste. Grate Pecorino Romano over to serve.