Preheat an oven to 350 degrees F.
Filling: Add the fruit to a large bowl and sprinkle with lemon juice, sugar and tapioca flour. Toss the ingredients until they are coated.
Dough: In a food processor, combine the flour, baking powder and sugars and pulse 3 to 4 times. Slowly pour in the buttermilk and mix until the dough comes together. Remove the dough from the processor and turn out on a lightly floured board. Divide the dough into 3/4 and 1/4 portions. Press the larger amount into the bottom of a 12-inch cast iron skillet. Add the filling and top with 6 to 8 even dollops of the remaining dough.
Topping: Sprinkle the dough tops with the cinnamon and sugar and evenly dot the butter over the cobbler. Put the skillet in the oven and bake until bubbly, about 50 minutes. Remove from the oven and let cool for 15 minutes. Serve hot.