In a bowl, whisk together the flour, sugar, and salt for the crust. Add the cold butter cubes and use a pastry cutter, fork, or your fingertips to work the butter into the flour until the mixture resembles coarse breadcrumbs with some pea-sized pieces of butter still visible—this creates those desirable flaky layers. Add the buttermilk and gently mix until just combined, then form the dough into a ball. Wrap it in plastic wrap and refrigerate for at least 1 hour (or up to overnight). I like to make this dough the night before so it's ready to go when I want to assemble the pie.

While the crust chills, peel and slice the peaches into 1/2-inch thick wedges—if you're having trouble peeling them, briefly blanch them in boiling water for 30 seconds, then transfer to ice water to loosen the skins. In a large bowl, combine the sugar, flour, cornstarch, and cinnamon. Add the peach slices and lemon juice, then gently toss until the peaches are evenly coated with the thickening mixture. Set aside; the peaches will begin releasing their juices.

Remove the chilled dough from the refrigerator and roll it out on a lightly floured surface into a 12-inch circle, about 1/8-inch thick. Transfer it to a 9-inch pie dish, letting the excess hang over the edges slightly. Trim the overhang to about 1 inch and crimp the edges decoratively with your fingers or a fork. Prick the bottom and sides with a fork several times to prevent excessive puffing. Freeze the crust for at least 15 minutes while you prepare the other components.

In a bowl, whisk together the flour, sugar, baking powder, baking soda, and salt. Add the cold cubed butter and use a pastry cutter or fork to work it into the dry ingredients until the mixture resembles coarse crumbs. Add the buttermilk and vanilla extract, stirring gently until just combined—the batter should be thick and slightly lumpy, like biscuit dough. Don't overmix, as this keeps the topping tender and fluffy.

Preheat your oven to 400°F. Remove the frozen pie crust from the freezer and pour the peach filling from Step 2 into it, spreading it evenly. Drop spoonfuls of the cobbler topping from Step 4 over the peaches, leaving some small gaps so steam can escape and you can see the fruit peeking through—this creates that rustic, cobbled appearance. Sprinkle the cinnamon sugar evenly over the top.

In a small bowl, whisk the egg with water to create an egg wash. Lightly brush the egg wash over the cobbler topping for a beautiful golden-brown finish—this step is optional but gives the top a bakery-quality appearance. Place the assembled pie on a baking sheet (to catch any drips) and bake at 400°F for 45 to 60 minutes, until the topping is golden brown and the filling is bubbling around the edges. If the crust or topping browns too quickly, loosely tent the pie with foil partway through baking.

Remove the pie from the oven and let it cool on a wire rack for at least 20 minutes before serving—I recommend waiting the full 20 minutes so the filling sets slightly and you get cleaner slices. The pie is wonderful served warm with vanilla ice cream or fresh whipped cream. Any leftovers can be stored covered at room temperature for up to 2 days or in the refrigerator for up to 4 days.