In a large bowl, whisk together flour, sugar, baking powder, salt, cinnamon and nutmeg until combined.
Whisk in milk and vanilla extract until smooth, then fold in diced peaches.
Pour filling into greased baking dish, then pour topping on top.
Place in oven and bake for 50-55 minutes, covering with aluminum foil, if necessary, until cooked through.
Remove from oven and let cool 15 minutes before serving.
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