In a medium Dutch oven, melt the butter over medium-high heat. Add the diced carrot and diced celery. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes. This base of sautéed vegetables adds great flavor to your soup.
Add the chicken broth, condensed cream of chicken soup, onion powder, and garlic powder to the pot with the sautéed vegetables. Stir to combine and dissolve the soup. Then, gently stir in the shredded cooked chicken. Cover the pot and bring the mixture to a simmer over medium-high heat, about 15 minutes. I like to give the soup a good stir halfway through to ensure everything is evenly combined.
While the soup base comes to a simmer, combine the Bisquick baking mix and whole milk in a medium bowl. Stir together until a wet, sticky dough forms. Don't worry if the mixture looks a bit wet—it helps keep the dumplings tender. I sometimes let the dough rest for a couple of minutes to hydrate the baking mix fully.
Reduce the heat to medium. Scoop the dumpling batter into ping pong ball-sized portions (about 1 1/2 tablespoons each) and drop them directly into the simmering soup in a single layer. Cover the pot and cook undisturbed for about 10 minutes, until the dumplings are cooked through. Uncover and check for doneness by poking a dumpling—there should be no wet dough in the center. If not cooked through, re-cover and cook 2–3 minutes more. To prevent sticking, I like to very gently push the dumplings apart with the back of a spoon after a few minutes of cooking.
Ladle the hot soup into bowls, ensuring each serving gets two or three dumplings. Top with chopped fresh parsley if desired, for a fresh, bright flavor and color. Leftovers should be kept in an airtight container in the fridge for up to 3 days; the dumplings may soften but the dish will still be delicious when reheated.