In a large stockpot, heat the olive oil over medium heat. Add the diced onion and garlic, and sauté until the onion becomes translucent, about 3-4 minutes.
Add the cubed chicken to the pot and cook until the chicken is lightly browned, about 5 minutes.
Stir in the carrots and celery, cooking for another 5 minutes until they start to soften.
Pour in the chicken broth, followed by the thyme, rosemary, and season with salt and pepper. Bring the mixture to a boil.
Reduce the heat to low and simmer for 15 minutes. Add the frozen peas and simmer for an additional 5 minutes.
In a mixing bowl, combine the flour, baking powder, and salt for the dumplings. Stir in the milk and egg until a dough forms.
Drop spoonfuls of the dumpling mixture into the simmering soup. Cover the pot and cook for an additional 10 minutes, allowing the dumplings to steam and rise.
Remove the pot from heat and let it sit for 5 minutes before serving.