Heat the butter and olive oil in a large pot over medium heat. Add the diced onion, sliced carrots, and sliced celery stalks. Sauté until the vegetables are softened, about 5 minutes.

Add the bay leaf and chicken broth to the pot. Bring the broth to a simmer.

Carefully place the boneless, skinless chicken breasts into the simmering broth. Cover the pot and let the chicken cook for about 15-20 minutes, or until it is cooked through and tender.

While the chicken is cooking, prepare the dumpling batter. In a mixing bowl, whisk together the eggs, all-purpose flour, and a pinch of salt until a thick batter forms.

Once the chicken is cooked, remove it from the pot and transfer it to a cutting board. Allow the chicken to cool slightly, then shred it into bite-sized pieces using two forks.

Return the shredded chicken to the pot of simmering broth. Stir in the chopped parsley and season the soup with salt and pepper to taste.

Using a spoon, carefully drop small portions of the dumpling batter into the simmering soup. Allow the dumplings to cook for about 10-15 minutes, or until they are cooked through and tender.

Once the dumplings are cooked, remove the pot from the heat. Discard the bay leaf.

Ladle the hot German Chicken Dumpling Soup into bowls and serve immediately, garnished with additional chopped parsley if desired. Enjoy this comforting and flavorful dish as a satisfying meal on its own or as a starter to a hearty German-inspired feast!