Heat the olive oil in a large pot or Dutch oven over medium heat. Add diced onion, sliced carrots, and sliced celery. Sauté for about 5 minutes until the vegetables are soft.
Add minced garlic and cook for an additional minute until fragrant.
Pour in the chicken broth and bring the mixture to a boil. Then, reduce the heat and let it simmer for about 15 minutes.
Stir in the shredded chicken, dried thyme, dried parsley, salt, and pepper. Allow the soup to simmer for another 5 minutes.
In a mixing bowl, combine the flour, baking powder, and salt for the dumplings. Stir in the milk, melted butter, and egg until just combined; do not overmix.
Drop spoonfuls of the dumpling batter into the simmering soup. Cover and cook for 10-12 minutes, until the dumplings are cooked through and fluffy.
Add the frozen peas to the soup and stir to combine. Cook for an additional 5 minutes.
Taste and adjust seasoning if necessary before serving.