Melt the butter in a large Dutch oven over medium heat. Add the carrot and celery and cook for about 5 minutes, stirring occasionally, until softened.
Stir in the chicken broth, cream of chicken soup, onion powder, and garlic powder. Add the shredded chicken, cover, and bring the mixture to a gentle simmer.
In a medium bowl, stir together the Bisquick and milk to form a soft dumpling batter.
Reduce the heat to medium. Scoop the batter into tablespoon-sized portions and drop them directly into the simmering soup in a single layer.
Cover the pot and cook for about 10 minutes without lifting the lid.
Check the dumplings for doneness. They should be firm and no longer doughy in the center. If needed, cover and cook for a few more minutes.
Ladle the chicken and dumplings into bowls and garnish with chopped parsley if desired.
