Melt butter in a microwavable dish. Pour 1 cup of sugar and flour into a mixing bowl, whisking in milk. Mix well. Then, pour in melted butter and whisk it all well together. Butter a baking dish.
Now rinse and pat dry the blackberries. Pour the batter into the buttered baking dish. Sprinkle blackberries over the top of the batter; distributing evenly. Sprinkle ¼ cup sugar over the top.
Bake in the oven at 350 degrees for 1 hour, or until golden and bubbly. If you desire, sprinkle an additional teaspoon of sugar over the cobbler 10 minutes before it’s done.