Prep the Peaches: Preheat oven to 350 degrees F. In a large bowl, combine peaches, brown sugar, white sugar, lemon juice, cinnamon, nutmeg, and cornstarch. Toss to coat.
Prepare the Baking Dish: Pour the peach mixture into a lightly greased 9x13-inch baking dish. Spread evenly.
Make the Topping: In another bowl, mix flour, sugar, baking powder, and salt. Stir in milk, melted butter, and vanilla until a thick batter forms.
Assemble: Spoon the batter evenly over the peach mixture. It won’t cover completely but will spread as it bakes.
Bake: Place the dish in the oven and bake for 40-45 minutes, or until the topping is golden brown and peaches are bubbling.
Cool and Serve: Let cool for 10-15 minutes before serving. Top with a scoop of vanilla ice cream for the ultimate finish.