In a large pot, combine potatoes, carrot, onion, celery, chicken broth, cream of chicken soup, and water. Bring to a boil, then reduce heat and simmer for 20-25 minutes, or until potatoes are tender.
Stir in cooked chicken and pepper (if using). Heat through.
Preheat oven to 400 degrees F (200 degrees C).
In a bowl, whisk together flour, baking powder, and salt.
Add milk and melted butter; stir until just combined.
Pour batter into a greased 8-inch square baking pan or cast iron skillet.
Bake for 20-25 minutes, or until golden brown.
Slice and serve warm with butter.