Start by preheating your oven to 350°F. Grease your 9x13-inch baking dish so nothing sticks once the filling starts bubbling. This small step saves you from a messy cleanup later on.
In a large bowl, stir together your chopped peaches, brown sugar, cornstarch, lemon juice, vanilla, and the spices. Pour this mixture into your prepared baking dish and spread it out evenly. The lemon juice keeps everything tasting bright instead of one-note sweet.
Slide the peach filling into the oven and bake it alone for about 10 minutes. This step softens the peaches so they aren't still firm once the biscuit topping is fully baked. Keep the oven on for the next stage.
While the peaches bake, whisk your flour, sugar, baking powder, baking soda, and salt together. Cut in the cold butter until the mixture looks like small crumbles. Pour in the cold buttermilk and stir gently just until it comes together.
Take small handfuls of the biscuit dough and flatten them into rough patties. Lay these pieces over the warm peach filling, covering most of the surface. It doesn't need to look perfect since this is meant to be a rustic dessert.
Brush the tops of the biscuit dough with your egg wash, then sprinkle the cinnamon sugar over everything. This little touch gives the topping a shiny golden color and a light, crisp crunch once baked.
Return the dish to the oven and bake for 40 to 50 minutes. You'll know it's ready when the topping turns golden brown and the peach filling bubbles around the edges. A toothpick inserted into the biscuit should come out clean.
Let the cobbler rest on a cooling rack for about 5 minutes once it comes out of the oven. This short rest helps the syrupy peach juices settle so every scoop holds together nicely when you serve it.