Preheat the oven to 400 degrees. Prepare the fruit mixture: wash the peaches and blueberries thoroughly. Cut the peaches into pieces roughly 1 inch in size. Mix the sugars, flour, orange juice, cinnamon, ginger, and salt together in a large bowl (it’ll form a granular paste). Add the fruit and stir gently to combine. Arrange the fruit in one layer in a cast-iron skillet or other deep-sided baking dish.
Make the biscuit dough: Combine the flour, cornmeal, sugar, baking powder, and salt together in a medium bowl. Cut the chilled butter into small pieces. Incorporate the butter into the flour mixture with a fork (I find smooshing some of the bigger pieces of butter against the side of the bowl helps separate it into flaky pieces). Finally, add the buttermilk and briefly stir until just incorporated (don’t overmix; the dough will be sticky).
Use a spoon to portion the biscuit dough over the prepared fruit. Organizing this is easier if you start with a ring of biscuits around the outside of the skillet, finishing with the biscuits on the interior portion of the cobbler. Bake in the oven until the biscuits are browned on top and the fruit is bubbly, about 35 minutes, rotating the skillet halfway through. Allow to cool slightly before serving (the fruit filling will be quite hot).