2. In a small bowl, mix the brown sugar and cornstarch together.
3. Place the peaches and blackberries in a medium sized saucepan and stir in the sugar mixture. Bring the mixture to a simmer and cook for 2 minutes, stirring frequently. Pour the mixture into a 2-quart baking dish and set aside.
4. In a food processor, combine the flour, sugar, baking soda and salt. Add the butter and process until the butter is the size of small peas. With the motor running, add the buttermilk in a steady stream and process for 5 seconds.
5. Turn the dough out onto a lightly floured surface and knead lightly until the dough comes together in a ball. Roll out the dough until it is about 1/3-inch thick and is wide enough to cover the top of the baking dish. Place the dough on top of the fruit mixture and, using a sharp paring knife, cut the dough to fit just inside the dish.
6. Cut a few slits (air vents) in the dough, place the dish on a cookie sheet and bake until the crust is golden brown, about 30 to 40 minutes. Let cool.
7. Serve the cobbler warm or at room temperature, with or without frozen yogurt.