Step 1: Prepare the Chicken and Broth

1. In a large pot or Dutch oven, melt butter over medium heat.
2. Add onions, carrots, and celery, sautéing until softened (about 5 minutes).
3. Stir in garlic and cook for another minute.
4. Pour in chicken broth, add bay leaves and thyme, and bring to a boil.
5. Submerge chicken into the broth, reduce heat, and simmer for 20-25 minutes until fully cooked.
6. Remove chicken, shred with two forks, and return to the pot.

Step 2: Thicken the Soup

1. In a small bowl, mix flour with water to form a slurry.
2. Gradually stir the slurry into the soup to thicken.
3. Pour in milk or heavy cream, stirring to combine.
4. Season with salt, pepper, and additional herbs as needed.

Step 3: Make the Dumplings

1. In a bowl, whisk together flour, baking powder, salt, and parsley.
2. Slowly mix in milk or water until a dough forms.
3. If using an egg, beat it separately and mix into the dough.
4. Drop spoonfuls of dough into the simmering soup.
5. Cover and cook for 10-12 minutes, until dumplings puff up and are cooked through.

Step 4: Final Touches

1. Gently stir to distribute dumplings evenly.
2. Remove bay leaves.
3. Garnish with fresh parsley and serve warm.