To make the dumplings, whisk together the flour, baking powder, and salt in a medium bowl.
Stir in the milk until well combined. Set the batter aside.
To make the soup, heat the olive oil in a large pot over medium heat.
Season the chicken with salt and pepper, then add it to the pot and cook for about 5 minutes per side, or until browned.
Remove the chicken from the pot and set it aside on a plate.
Add the onion, carrots, and celery to the pot and cook for 5 minutes, or until the vegetables are softened.
Pour in the chicken broth and add the bay leaf. Bring the soup to a boil, then reduce the heat to low and let it simmer for 10 minutes.
Add the chicken back into the pot, along with any juices that have accumulated on the plate. Increase the heat to medium and let the soup simmer for 10 minutes.
To make the dumplings, use a spoon to drop the batter by the tablespoon into the soup. Cook for 5 minutes, or until cooked through.
Remove the bay leaf from the pot and stir in the chopped parsley.