In a large pot, combine the ham hocks, onions, celery, carrots, and water. Bring to a boil. Reduce the heat to medium-low and simmer until the meat starts to fall from the bones, about 1 1/2 hours. Remove from the heat and strain through a colander into a clean pot. Set the ham hocks aside to cool.

To the stock, add the black beans, chiles, cumin, and chili powder and bring to a boil. Reduce the heat to medium and cook at a brisk simmer until the beans are tender, about 1 1/2 hours, skimming the surface to remove any foam. Add 1/2 teaspoon of salt during the last 5 minutes of cooking time. While the beans are cooking, remove the meat from the ham hocks and coarsely chop. Reserve 1/2 cup of meat and add the rest (about 2 1/2 cups) to the black beans.

In a bowl, combine the reserved 1/2 cup of meat with the flour, egg, beer, baking powder, and remaining 1/2 teaspoon salt. Mix to form a batter. Drop the batter 1 tablespoon at a time onto the top of the soup to form 10 dumplings. Return to medium heat, cover and cook undisturbed for 2 to 3 minutes.

To serve, spoon 1 dumpling into each soup bowl and ladle about 1 cup of soup over the dumpling.