Preheat the oven to 350°F. Put the butter in a 9 x 13- inch baking dish and place in the oven to melt. Once melted, remove from the oven. Keep the oven on.

To make the peaches, combine the sliced peaches, sugar, cinnamon, nutmeg, lemon juice, and cornstarch in a bowl and toss well. Set aside.

To make the batter, combine the flour, sugar, baking powder, and salt in a bowl. Stir in the milk, egg, and vanilla. Pour the batter over the melted butter.

Arrange the peach slices on top of the batter. Sprinkle the remaining sugar over the entire cobbler. Bake for 25 to 30 minutes, until the top is golden brown and the cake begins to pull away from the sides of the baking dish. Remove to a wire rack to cool for 10 minutes before serving.

Spoon a scoop of ice cream over each serving.