In a large pot, heat the olive oil over medium heat. Add the chopped onion and cook until translucent, about 5 minutes.
Stir in the minced garlic, sliced carrots, and celery. Cook for an additional 5-7 minutes until the vegetables are softened.
Add the dried thyme, dried rosemary, salt, and pepper to the pot. Stir to combine.
Pour in the chicken broth and bring the mixture to a boil.
Add the chicken pieces to the pot and reduce the heat to a simmer. Cook for 15-20 minutes until the chicken is fully cooked and tender.
Stir in the frozen peas and cook for another 5 minutes.
While the chicken mixture is simmering, prepare the dumplings. In a mixing bowl, combine the flour, baking powder, and salt.
Add the milk and melted butter to the dry ingredients and stir until just combined.
Drop spoonfuls of the dumpling batter onto the simmering chicken mixture. Cover the pot and cook for 15 minutes without lifting the lid, allowing the dumplings to steam.
Once the dumplings are cooked through, serve the chicken and dumplings hot, garnished with fresh herbs if desired.
Notes
For added flavor, consider using homemade chicken broth.