Preheat your oven to 375°F (190°C). Grease a 9×13-inch baking dish with butter or non-stick spray.
Combine peaches, granulated sugar, brown sugar, cinnamon, nutmeg (if using), lemon juice, and cornstarch in a large bowl. Pour into the prepared baking dish.
Whisk together flour, granulated sugar, baking powder, and salt. Stir in melted butter, milk, and vanilla extract until smooth.
Pour the batter over the peach filling. Optionally sprinkle with cinnamon or sugar.
Bake for 40–45 minutes, or until the topping is golden brown and the filling is bubbling.
Allow to cool for 10 minutes before serving. Serve warm with vanilla ice cream or whipped cream.
Notes
For the best flavor, use fresh peaches. If using canned peaches, drain thoroughly before using.