Preheat the oven to 350 degrees F. Place the butter in a large casserole dish or cast-iron skillet and place in the oven to melt, 5 to 7 minutes. If the peaches are not juicy and sweet, sprinkle them with some of the sugar and set aside.
Whisk together the flour, baking powder and salt in a medium bowl. Add the remaining sugar, the milk and vanilla extract; whisk until evenly blended.
Remove the dish from the oven and add the melted butter to the batter. Then, immediately pour the batter all at once back into the dish. Add the peaches and any juices into the center of the batter. Gently shake the dish to evenly distribute the peaches.
Return to the oven and bake until the top is golden brown and a cake tester poked into the batter comes out clean, about 30 minutes. Serve hot, warm or at room temperature with freshly whipped cream or ice cream.