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, sliced carrots, and chopped celery, then cook for an additional 5 minutes until the vegetables soften.
Add the chicken pieces to the pot, seasoning with salt, pepper, thyme, and parsley. Cook for about 5-7 minutes, stirring occasionally, until the chicken is browned on all sides.
Pour in the chicken broth and add the bay leaf. Bring the mixture to a simmer, cover, and reduce heat to low. Let it simmer for about 20 minutes.
In a large bowl, whisk together the flour, baking powder, salt, and pepper. Stir in the chopped parsley and thyme.
In a separate bowl, mix together the buttermilk and melted butter. Gradually fold the wet ingredients into the dry ingredients until just combined. The dough should be slightly sticky.
After the chicken has simmered for 20 minutes, gently fold in the frozen peas. Carefully drop spoonfuls of the dumpling dough over the surface of the stew.
Cover the pot with a lid (do not lift the lid during cooking), and let the dumplings steam in the stew for about 15-20 minutes, or until they are puffed up and cooked through.
Once the dumplings are cooked, remove the bay leaf. Taste the stew and adjust the seasoning if necessary.
Ladle the chicken and dumplings into bowls and garnish with additional fresh parsley before serving.