Toss the blackberries with the sugar in a large bowl. Let sit 30 minutes.
Heat the oven to 375 degrees. Put the butter in an 8-inch square baking dish and stick the dish in the oven.
While the butter melts, whisk together the flour and milk in another bowl, plus any juice that's come out of the berries.
When the butter is melted and bubbling, remove the pan from the oven. Pour the flour mixture over the butter - do not stir.
Pour the sugared berries on top of the batter, again without stirring.
Return the pan to the oven and bake 30-40 minutes, until the cobbler is bubbling and the juices threaten to escape the pan.
Cool 15 minutes in the pan before serving. Whipped cream is always welcome on top of blackberry cobbler.
