In a large bowl, combine ground beef, ground chicken, chopped onion, minced garlic, chopped parsley, 1/2 teaspoon salt, 1/4 teaspoon black pepper, and dried thyme. Mix well until all ingredients are evenly incorporated.
Form the meat mixture into small meatballs about 1 inch in diameter and set aside.
In a large pot, bring the chicken broth to a boil over medium-high heat.
Add the diced carrots and celery to the broth and simmer for 5 minutes.
Carefully add the meatballs to the simmering broth. Reduce heat to medium-low and cook for 15 minutes, or until the meatballs are cooked through.
While the meatballs cook, prepare the dumpling batter. In a medium bowl, whisk together the flour, baking powder, and 1/2 teaspoon salt.
Add the milk and melted butter to the dry ingredients and stir until just combined. Do not overmix; the batter should be thick but spoonable.
Drop spoonfuls of the dumpling batter (about 1 tablespoon each) onto the simmering soup. Cover the pot with a lid and cook for 15 minutes without lifting the lid, until the dumplings are puffed up and cooked through.
Remove the soup from heat and let it rest for 5 minutes before serving.
Ladle the soup into bowls, ensuring each serving has meatballs, vegetables, and dumplings. Serve hot.