1. Melt the butter in a large pot or deep skillet over medium heat. Add the onion, carrots, and celery, then cook for 5 to 6 minutes until softened.

2. Stir in the garlic and cook for 30 seconds, just until fragrant.

3. Sprinkle in 1/4 cup flour and stir well to coat the vegetables.

4. Slowly pour in the chicken broth while stirring, then add 1 cup milk, 1 teaspoon salt, 1/2 teaspoon black pepper, and 1/2 teaspoon dried thyme.

5. Bring the mixture to a gentle simmer, then stir in the shredded chicken.

6. In a medium bowl, whisk together 2 cups flour, baking powder, and 1/2 teaspoon salt.

7. Add 3/4 cup milk and 2 tablespoons melted butter to the dumpling mixture, then stir just until a soft dough forms.

8. Drop spoonfuls of dumpling dough over the simmering chicken mixture.

9. Cover the pot with a tight-fitting lid and cook on low for 15 to 18 minutes, or until the dumplings are puffed and cooked through.

10. Let the pot rest for 2 to 3 minutes, then serve hot with extra black pepper if desired.