Preheat oven to 375°F (190°C). Place butter pieces in a 9x13-inch baking dish and set in the oven while it preheats, about 5 minutes, until fully melted. Watch closely so it does not brown.
Combine peaches, 3/4 cup sugar, lemon juice, cinnamon, nutmeg, and cornstarch in a large bowl. Stir to coat every slice. Let sit 10 minutes until a syrup forms at the bottom of the bowl.
In a separate bowl, whisk together the flour, 1 cup sugar, baking powder, and salt. Add the milk and vanilla extract. Whisk until the batter is smooth with no dry flour remaining.
Remove the hot baking dish from the oven. Pour the batter evenly over the melted butter. Do not stir. Spoon the peach mixture over the batter in an even layer, then pour any collected syrup from the bowl on top. Do not stir.
Bake at 375°F (190°C) for 40 to 45 minutes, until the topping is deep golden brown and a toothpick inserted into the batter between the fruit pieces comes out clean. The filling should be visibly bubbling at the edges.
Remove from the oven and rest for 10 to 15 minutes before scooping and serving.
