Get Ready: Preheat your oven to 350°F (177°C). Lightly grease a 9x13 inch baking pan.
Make the Peach Filling: In a large bowl, combine the sliced peaches, brown sugar, cornstarch, lemon juice, vanilla, cinnamon, nutmeg, ginger, and salt. Stir until the peaches are evenly coated.
Pre-bake the Filling: Spread the peach mixture into your prepared baking pan. Bake for 10 minutes. This helps the filling get juicy. Remove from the oven and set aside. Keep the oven on.
Mix the Dry Topping Ingredients: While the peaches bake, grab another large bowl. Whisk together the flour, granulated sugar, baking powder, baking soda, and salt.
Cut in the Butter: Add the small cubes of cold butter to the flour mixture. Using a pastry cutter or two forks, work the butter in until you have coarse, pea-sized crumbles.
Add Buttermilk: Pour in the cold buttermilk. Mix gently with a fork or spatula just until a soft dough comes together. Do not overmix.
Assemble the Cobbler: Grab clumps of the biscuit dough and flatten them into small patties with your hands. Lay these patties over the top of the warm peach filling, covering most of the fruit.
Add Finishing Touches: Gently brush the top of the dough with the egg wash mixture. Sprinkle the cinnamon-sugar evenly over the top.
Bake: Bake for 40 to 50 minutes, or until the topping is golden brown and the filling is bubbling around the edges. A toothpick inserted into a biscuit should come out clean.
Cool and Serve: Let the cobbler cool on a wire rack for at least 10 minutes before serving. This allows the filling to set. Serve warm.