Preheat oven to 350 degrees. Place butter in a 13x9 baking dish and put in oven until butter is melted. Remove.
Sweeten blackberries with 1/2 cup sugar, depending on their tartness. You do not want them too sweet. Stir in cinnamon.
Mix sugar, self-rising flour and milk until smooth. Pour over melted butter. Spoon fruit over batter and do not stir.
Bake for about 1 hour or until golden and done. Serve warm with ice cream.