Heat olive oil in a large pot or Dutch oven over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5 minutes until the vegetables soften.
Add minced garlic and cook for an additional 1 minute until fragrant.
Pour in the chicken broth and bring to a boil. Add the shredded chicken, thyme, rosemary, salt, and pepper. Reduce the heat and simmer for about 15 minutes.
In a mixing bowl, combine the flour, baking powder, garlic powder, and salt.
In another bowl, whisk together the milk and melted butter. Pour the wet ingredients into the dry ingredients and stir until just combined to form a dough.
Once the soup has simmered for 15 minutes, drop spoonfuls of the dumpling dough into the bubbling broth. Cover the pot and let the dumplings cook for about 10-12 minutes, until they are fluffy and cooked through.
Add the frozen peas and stir gently. Cook for an additional 2-3 minutes until heated through.
Adjust seasoning with salt and pepper as needed. Serve the soup hot, garnished with fresh parsley if desired.