In a large mixing bowl, combine ground beef, ground chicken, finely chopped onion, minced garlic, chopped parsley, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and 1/4 teaspoon dried thyme. Mix well until all ingredients are evenly incorporated.
Add the all-purpose flour to the meat mixture, then gradually add cold water while stirring until a soft dough forms. Set aside.
In a large pot, heat olive oil over medium heat. Add diced onion, carrots, and celery. Cook, stirring occasionally, until vegetables are softened, about 5 minutes.
Add minced garlic to the pot and cook for 1 minute until fragrant.
Pour in the chicken broth and bring to a boil.
Using a teaspoon, drop small dumplings (about 1 tablespoon each) from the meat mixture directly into the boiling broth.
Reduce heat to a simmer and cook for 25 minutes, or until dumplings are cooked through and vegetables are tender.
Season the soup with 1/2 teaspoon salt, 1/4 teaspoon black pepper, and 1/4 teaspoon dried thyme. Stir well.
Ladle soup into bowls and serve hot.