In a large bowl, combine the ground beef, egg, breadcrumbs, salt, pepper, nutmeg, and chopped parsley. Mix gently until just combined. Form into small, bite-sized meatballs and set aside.
In a large Dutch oven, heat the olive oil over medium heat. Add the diced onion, carrots, celery, and leek. Cook for 5–7 minutes until the vegetables are softened.
Pour in the broth and bring the soup to a gentle boil.
Carefully drop the meatballs into the boiling broth. Reduce the heat to a simmer and cook uncovered for 15 minutes, or until the meatballs are cooked through.
Add the vermicelli noodles to the soup. Cook according to package instructions, usually about 5–7 minutes.
Stir in the frozen peas and cook for 2–3 minutes until heated through. Season the soup with additional salt and pepper to taste.
Ladle the soup into bowls and garnish with fresh parsley before serving.