Preheat the Oven:
Preheat your oven to 375°F (190°C) and grease a 9x13-inch baking dish.
Prepare the Peach Filling:
In a mixing bowl, combine the sliced peaches, granulated sugar, brown sugar, lemon juice, cinnamon, nutmeg, and cornstarch. Mix well to coat the peaches evenly, then pour the mixture into the prepared baking dish.
Make the Cobbler Topping:
In another bowl, whisk together the flour, sugar, baking powder, and salt. Stir in the melted butter, milk, and vanilla extract until smooth.
Assemble the Cobbler:
Pour the topping over the peaches, spreading it out evenly. Some peaches will still be visible, which is fine.
Bake the Cobbler:
Bake for 40-45 minutes or until the topping is golden brown and the filling is bubbling.
Cool and Serve:
Let the cobbler cool for 5-10 minutes before serving. Pair with vanilla ice cream or whipped cream for an extra special treat.