In a large pot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion, minced garlic, sliced carrots, and sliced celery. Sauté for about 5 minutes, until the vegetables are softened.
Stir in the dried thyme, dried rosemary, and bay leaves, cooking for another minute until fragrant. Add the chicken pieces to the pot and cook for about 5 minutes, until they are no longer pink on the outside.
Pour in the chicken broth and bring the mixture to a boil. Reduce the heat to low and let it simmer for about 15 minutes, or until the chicken is cooked through.
While the chicken stew is simmering, prepare the dumpling dough. In a mixing bowl, whisk together the flour, baking powder, and salt. Add the milk and melted butter, stirring just until the dough comes together. Be careful not to overmix.
Stir the frozen peas into the chicken stew. Season the stew with salt and pepper to taste. Using a spoon, drop heaping tablespoons of the dumpling dough onto the surface of the simmering stew. Make sure to space the dumplings slightly apart as they will expand as they cook.
Cover the pot with a lid and let the dumplings cook for about 15 minutes, or until they are puffed up and cooked through. Do not lift the lid while the dumplings are cooking to ensure they cook evenly.
Remove the bay leaves from the stew. Ladle the chicken and dumplings into bowls, and garnish with chopped fresh parsley if desired.