Place the butter into a 20x20cm baking dish and place into the oven until melted. Stir the sugar, nutmeg and self-raising flour together in a mixing bowl. Stir in the milk until no lumps remain. Pour the batter over the melted butter in the baking dish. Do not stir. Spoon the sliced peaches over top; gently pour in the juice.
Return to the oven and bake until the batter has firmed and the cobbler has risen a bit, 35 to 45 minutes.