Gently wash and pick through the fresh blackberries, discarding any stems or bruised berries; then, in a large bowl, combine them with sugar, flour, and lemon juice and toss until evenly coated.

In a separate bowl, whisk together the flour, sugar, baking powder, and salt. Cut in the cold butter until the mixture resembles coarse crumbs, then stir in the milk until just combined, forming a soft dough.

Pour the blackberry mixture into a 9x13 inch baking dish, then drop spoonfuls of the dough evenly over the fruit. Bake in a preheated oven at 375°F (190°C) for 40-45 minutes, or until the topping is golden brown and the filling is bubbling.

Let the cobbler cool slightly before serving warm, optionally with a scoop of vanilla ice cream.