Preheat the oven to 400º F and lightly grease a 9×13-inch baking dish with butter or non-stick spray.
In a large saucepan over medium heat, whisk together brown sugar, granulated sugar, and nutmeg. Mix in butter and water and bring to a boil, stirring until the sugar is fully dissolved. Remove from heat and set aside.
In a large bowl, whisk together flour, sugar, baking powder, sea salt, cinnamon, and nutmeg until combined.
Add milk and vanilla extract to the dry ingredients, and whisk until smooth.
Fold in diced peaches.
Pour the filling into the greased baking dish, and then pour the topping on top.
Bake for 50-55 minutes, covering with aluminum foil if necessary, until cooked through.
Remove from the oven and let cool for 15 minutes before serving.
Notes
Optional: Garnish with ice cream, whipped cream, or cool whip.