In a large pot, heat the olive oil over medium heat. Add the chopped onion, diced carrots, and diced celery. Sauté the vegetables, stirring occasionally, until they are softened and the onion is translucent, about 5-7 minutes.
Add the minced garlic and continue to cook for an additional 1-2 minutes, stirring frequently, until the garlic becomes fragrant but not browned.
Pour in the chicken broth and bring the mixture to a gentle boil.
Stir in the shredded chicken, dried thyme, and black pepper. Season with a pinch of salt, being cautious as the broth may already be salty. Reduce the heat to a low simmer and let it cook for about 10 minutes to blend the flavors.
While the soup simmers, prepare the dumpling dough: In a medium mixing bowl, whisk together the all-purpose flour, baking powder, and 1/2 teaspoon of salt. Slowly pour in the milk while stirring, until just combined into a soft dough; avoid overmixing.
Using a spoon, carefully drop dollops of the dumpling mixture into the simmering soup. Cover the pot with a lid and let the dumplings steam above the soup for about 15 minutes. Avoid lifting the lid during this time to ensure the dumplings cook properly.
After 15 minutes, gently stir in the frozen peas and allow the soup to cook for an additional 5 minutes, until the peas are warmed through and the dumplings are fluffy and cooked.
Taste the soup and adjust the seasoning with additional salt or pepper if necessary. Just before serving, fold in the chopped fresh parsley for a burst of flavor.