Begin by preheating your oven to 350°F (177°C) and lightly greasing a 9×13-inch baking dish, although any 3-4-quart dish will suffice.
To prepare the filling, combine all filling ingredients in a large bowl and transfer the mixture to your prepared baking dish. Bake this layer for 10 minutes, then remove from the oven and set aside while you prepare the biscuit topping. Keep the oven turned on.
For the biscuit topping, in a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt. Using either a pastry cutter or two forks, cut in the butter until the mix looks like coarse crumbs, pea-sized. If available, a pastry cutter simplifies this process significantly, though a food processor is an alternative. Gradually pour in the buttermilk and stir gently until the mixture is just combined and slightly sticky. If the mixture feels too dry, incorporate an additional tablespoon of buttermilk.
To assemble the cobbler, take portions of the dough and flatten them slightly with your hands. Arrange these pieces over the warm peach mixture, ensuring to cover most of the surface.
Brush the biscuit topping with the prepared egg wash and, if desired, sprinkle with the cinnamon-sugar mixture.
Return the dish to the oven and bake for 40-50 minutes. The cobbler is ready when the topping is golden brown and the peach filling bubbles at the edges. Check doneness by inserting a toothpick into the biscuit—if it emerges clean, the cobbler is baked through.
Once baked, remove the cobbler from the oven and place it on a wire rack to cool for about 5 minutes before serving. This dish is best served warm, accompanied by a scoop of vanilla ice cream or a dollop of whipped cream.
Store any leftovers in the refrigerator, covered, for up to 5 days. Enjoy your delicious creation repeatedly!