01 - Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the diced onion, sliced carrots, and sliced celery. Sauté until the vegetables are softened, about 5 minutes. Add the minced garlic and cook for 1 minute more, stirring frequently.
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. Let the stew simmer uncovered for 15 minutes to allow the flavors to meld.
04 - While the stew simmers, whisk together the all-purpose flour, baking powder, baking soda, salt, and chopped fresh parsley in a mixing bowl. Pour in the melted butter and whole 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 stew. Stir in the frozen peas and heavy cream if using, then return the liquid to a gentle simmer.
06 - Drop spoonfuls of the dumpling dough, about 1 tablespoon each, onto the surface of the simmering stew. Space them evenly apart so they have room to expand. Cover the pot tightly with a lid and cook over low heat for 18 to 20 minutes. Do not lift the lid during this time. The dumplings should be puffed up and cooked through when done.
07 - Taste the stew and adjust the salt and pepper as needed. Ladle into bowls, ensuring each serving gets plenty of chicken, vegetables, and dumplings. Garnish with additional fresh parsley if desired and serve hot.