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. Add the minced garlic, thyme, rosemary, salt, and pepper, and cook for another minute until fragrant.

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 in the heavy cream and let it simmer for about 10 minutes.

While the soup is simmering, prepare the dumplings. In a medium bowl, whisk together the flour, baking powder, and salt. Add the milk and stir until just combined; do not overmix.

Drop spoonfuls of the dumpling batter into the simmering soup. Cover the pot and let the dumplings cook for about 15 minutes without lifting the lid.

Once the dumplings are cooked through, remove the pot from heat. Garnish with fresh parsley before serving.