Preheat your oven to 350°F. Grease a 2-quart baking dish with butter.
In a large bowl, combine the sliced peaches with 2 tablespoons of sugar and stir gently. Allow them to sit for 10 minutes.
In another mixing bowl, whisk together the flour, remaining sugar, baking powder, salt, cinnamon, and nutmeg until well combined.
Add the melted butter and vanilla extract to the dry ingredients. Stir until just combined—do not overmix.
Spread the peach mixture evenly in the prepared baking dish, then dollop the batter over the peaches.
Bake in the preheated oven for 30 to 35 minutes, or until the topping is golden brown and bubbling.
Remove from the oven and allow to cool for about 15 minutes before serving.
Serve warm, preferably with a scoop of vanilla ice cream.