Preheat oven to 375°F and lightly grease your 8 x 8 inch pan.
In a small saucepan over the stove or in a microwave, melt the butter. Set aside to cool.
In a large bowl, add the flour, baking powder, and salt. Whisk to combine.
Add the milk, sour cream, and the melted butter to the bowl, and whisk to combine. The consistency should be like cake batter.
Pour this into the 8 x 8 inch pan and smooth out the top, making sure it is evenly in the pan.
Pour the blackberries over the batter. They should cover almost every inch of the batter. Push some into the batter, just a bit.
Sprinkle the sugar over top of the blackberries, making sure to evenly distribute it across the entire pan.
Bake in the preheated oven for 50 minutes or until the fruit is bubbling and the top is slightly browned.
Serve immediately with ice cream. Be careful not to burn your mouth!