01 - Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the diced onion, sliced carrots, and celery. Sauté until the vegetables have softened, approximately 5 minutes. Add the minced garlic and cook for an additional 1 minute until fragrant.
02 - Add the bite-sized chicken pieces to the pot. Season with salt, pepper, dried thyme, and dried parsley. Sauté until the chicken is lightly browned on all sides, about 3 to 4 minutes.
03 - Pour in the chicken broth and drop in the bay leaf. Bring the liquid to a gentle boil, then reduce the heat to medium-low and let the stew simmer for 15 minutes so the flavors meld together.
04 - While the stew simmers, whisk together the all-purpose flour, baking powder, baking soda, salt, and chopped parsley in a mixing bowl. Pour in the melted butter and milk, stirring gently until just combined. Be careful not to overmix, as this will make the dumplings tough.
05 - Remove and discard the bay leaf from the simmering pot. Stir in the frozen peas and heavy cream if using. Allow the mixture to return to a gentle simmer.
06 - Drop spoonfuls of the dumpling dough, approximately 1 tablespoon each, onto the surface of the simmering stew, spacing them about 1 inch apart. Cover the pot with a tight-fitting lid and cook over low heat for 18 to 20 minutes. Resist lifting the lid during cooking. The dumplings are ready when they are puffed, fluffy, and cooked through.
07 - Taste the finished stew and adjust the salt and pepper as needed. Ladle into bowls, ensuring each serving gets a generous portion of chicken, vegetables, broth, and dumplings. Garnish with additional fresh parsley if desired and serve hot.