Place blackberries in a large microwave safe mug and sprinkle 1 tablespoon of sugar over blackberries; set aside.
Meanwhile, place butter in a small microwave safe bowl. Microwave for 15-20 seconds, or until melted. Add flour, the remaining 2 tablespoons sugar, salt, baking powder and milk to the melted butter. Whisk until fully combined.
Pour batter over blackberries in mug and microwave for 2-3 minutes, or until cobbler has puffed up and is cooked through. Serve warm topped with ice cream, if desired.