In a large pot, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 3-4 minutes. Stir in the minced garlic, carrots, and celery, and cook for another 5 minutes until the vegetables are tender.
Add the dried thyme, dried rosemary, salt, and black pepper to the pot. Pour in the chicken broth and bring to a simmer.
Stir in the shredded chicken and frozen peas. Allow the mixture to simmer for about 10 minutes.
In a separate bowl, combine the flour, baking powder, and salt for the dumplings. Add the melted butter and 1/2 cup of milk, stirring until just combined.
Drop spoonfuls of the dumpling mixture onto the simmering chicken mixture. Cover the pot with a lid and let the dumplings cook for about 15 minutes without lifting the lid.
After 15 minutes, check the dumplings for doneness; they should be fluffy and cooked through. Serve hot.