In a large bowl, combine ground beef, ground chicken, finely chopped onion, minced garlic, chopped parsley, salt, black pepper, dried thyme, dried oregano, and the egg. Mix thoroughly until well combined.
Gradually add the all-purpose flour to the meat mixture, mixing until a soft dough forms that can be shaped into small dumplings.
Heat olive oil in a large pot over medium heat. Add diced onion, sliced carrots, and sliced celery. Sauté for 5-7 minutes until vegetables are softened.
Add minced garlic to the pot and cook for another 1 minute until fragrant.
Pour in the chicken broth and bring to a boil.
Using a teaspoon, drop small dumplings from the meat mixture into the boiling broth. Reduce heat to a simmer.
Simmer the soup for 25-30 minutes, or until the dumplings are cooked through and the vegetables are tender.
Taste the soup and season with additional salt and black pepper as needed.
Ladle the soup into bowls and serve hot.