Heat the olive oil in a large pot over medium heat. Add the diced onion and sauté until translucent, about 3-4 minutes.
Stir in the minced garlic, sliced carrots, and celery. Sauté for another 5 minutes until the vegetables begin to soften.
Add the dried thyme, dried rosemary, and season with salt and pepper. Mix well.
Place the chicken breasts in the pot, and pour in the chicken broth. Bring to a simmer and cook for 15 minutes until the chicken is cooked through.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken back to the pot along with the frozen peas.
In a mixing bowl, combine the flour, baking powder, and salt for the dumplings. Add the milk and melted butter, stirring until just combined.
Drop spoonfuls of the dumpling batter over the simmering soup. Cover the pot with a lid and let the dumplings steam for about 15 minutes, until they are fluffy and cooked through.
Serve the soup hot, garnished with fresh parsley for added flavor.