In a large pot over medium heat, heat 1 tablespoon olive oil; sauté 1 cup diced carrots, 1 cup diced celery, and 1 cup diced onion until softened, about 5 minutes.

Add 1 pound boneless, skinless chicken breasts and 4 cups chicken broth to the pot.

Stir in 1 teaspoon dried thyme, 1 teaspoon salt, and 1/2 teaspoon black pepper; bring to a boil.

Reduce heat to low and simmer, covered, for 20 minutes or until the chicken is cooked through.

Remove the chicken from the pot and shred with two forks, then return the shredded chicken to the pot.

In a mixing bowl, whisk together 2 cups all-purpose flour, 1 tablespoon baking powder, and 1 teaspoon salt; stir in 1 cup milk until just combined to form the dumpling batter.

Drop spoonfuls of the dumpling batter onto the simmering chicken mixture.

Cover the pot and cook over low heat for 15 minutes without lifting the lid to steam the dumplings.

Sprinkle 1/2 cup chopped fresh parsley over the finished dish and serve immediately.