In a large pot, heat the olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5 minutes until the vegetables are softened. Stir in the minced garlic, thyme, rosemary, salt, and pepper, cooking for an additional minute.
Pour in the chicken broth and bring the mixture to a boil. Once boiling, reduce the heat to a simmer and add the shredded chicken and frozen peas. Stir to combine and let it simmer for about 10 minutes.
In a separate bowl, whisk together the flour, baking powder, and salt. Add the milk and melted butter, stirring until just combined. The dough will be thick.
Drop spoonfuls of the dumpling batter into the simmering chicken mixture. Cover the pot and let the dumplings cook for about 15 minutes without lifting the lid.
After 15 minutes, carefully remove the lid. Stir in the heavy cream and let it simmer for an additional 5 minutes to thicken slightly.
Serve hot, garnished with fresh parsley.