Preheat your oven to 350°F (175°C) so it's ready when the cobbler is assembled.
In a large mixing bowl, combine the drained peaches, brown sugar, white sugar, vanilla extract, cinnamon, nutmeg, and lemon zest. Mix gently until well-coated.
Add the cornstarch slurry to the peach mixture and stir until fully incorporated. This will help the filling thicken beautifully as it bakes.
Roll out one pie crust and place it into the bottom of a baking dish, covering the base and slightly up the sides.
Bake for 10–12 minutes, until lightly golden to prevent sogginess.
Pour the peach filling over the pre-baked crust.
Cut the second pie crust into strips or shapes and place on top in a lattice pattern or your preferred design.
Drizzle the melted butter over the top crust for extra richness and golden color.
Bake for 40–45 minutes, or until the crust is golden brown and the filling is bubbling.
Let the cobbler rest for 10 minutes to allow the filling to set.
Serve warm—especially delicious with vanilla ice cream or whipped cream.