In a deep 8- or 9-inch skillet, combine berry mixture and bring to a simmer over moderate heat.
While berries are cooking, make the dumpling dough: In a mixing bowl, stir together the flour, sugar, baking powder, baking soda and salt. Stir in the melted butter. Add enough of the buttermilk to form a soft, sticky dough that is slightly wetter than a biscuit dough.
Using a soup spoon, place rounded spoonfuls of the dough over the fruit, forming small dumplings. Sprinkle the dumplings with the cinnamon sugar, to taste. Tightly cover the skillet with a lid or a sheet of foil and steam the mixture over medium-low heat, without opening the lid, until the dumplings are set and puffed and the surface is dry when touched, about 15 minutes.
To serve, spoon the warm grunt into serving bowls and top with whipped cream, ice cream or sweetened yogurt.