Heat olive oil or butter in a large pot over medium heat.

Add the onions, carrots, and celery, and sauté for 5 minutes until softened.

Stir in the garlic and thyme and cook for 1 minute until fragrant.

Pour in the chicken broth and bring to a gentle simmer.

Add the shredded chicken, salt, and pepper, and simmer for 10 minutes to blend the flavors.

In a medium bowl, whisk together the flour, baking powder, and salt.

Stir in the milk and melted butter until just combined; the dough should be slightly sticky.

Using a spoon, drop small mounds of dough into the simmering broth, spacing them about 2 inches apart.

Cover the pot with a lid and let the dumplings cook undisturbed for 15 minutes.

For a creamier broth, stir in ½ cup of heavy cream or create a slurry by mixing 2 tablespoons of flour with ¼ cup of water and stirring it into the broth.

Cook for 3-5 minutes until the broth thickens.

Serve the chicken and dumplings in bowls, garnished with fresh parsley.