Sauté Vegetables: In a large pot, melt butter over medium heat. Add onions, carrots, and celery. Cook until the onion is translucent, about 5-7 minutes. Add garlic and cook for 30 seconds.
Add Broth and Chicken: Pour in chicken broth and add shredded chicken. Season with salt, pepper, bay leaves, and parsley. Bring to a boil, then reduce to a simmer.
Prepare Dumplings: In a bowl, mix flour, baking powder, and salt. Grate cold butter into the flour mixture and stir to coat. Add milk and stir until a dough forms.
Add Dumplings to Soup: Drop 1-inch pieces of dough into the simmering soup. Cover and cook for 15-20 minutes until dumplings are cooked through.
Thicken Soup: Mix cornstarch and water to create a slurry. Pour into the soup, stirring until thickened.