Heat the olive oil in a large pot over medium heat. Add the diced onion and minced garlic, cooking until softened, about 3-4 minutes.
Stir in the carrots and celery and continue to cook for another 5 minutes until the vegetables are slightly tender.
Add the cubed chicken to the pot and cook until browned, about 5 minutes.
Pour in the chicken broth and add the thyme, parsley, salt, and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for about 15 minutes.
Stir in the frozen peas and cook for an additional 5 minutes.
In a mixing bowl, combine the flour, baking powder, and salt. Whisk together. Add the milk and melted butter, stirring gently until just combined. Be careful not to overmix.
Drop spoonfuls of the dumpling batter onto the simmering soup. Cover the pot with a lid and allow the dumplings to steam for about 10-12 minutes, until they are cooked through.
Serve the chicken and dumplings soup hot, ladled into bowls.