Add the blackberries, ½ tablespoon sugar, and lemon juice to a 10-ounce ramekin. Stir gently to coat the berries, then set aside.
Make the topping
In a small bowl, whisk the flour, 1 tablespoon sugar, baking powder, and salt.
Pour in the milk and whisk until the batter is smooth.
Pour the batter evenly over the blackberries.
Set the ramekin on a rimmed baking sheet.
Bake for 20 to 25 minutes, until the topping is golden brown and the berry juices bubble around the edges.
Notes
Use fresh berries when you can. Fresh blackberries hold their shape and give the filling the best flavor. If you only have frozen, thaw and drain them well first so the cobbler doesn't turn watery.Taste your berries before you start. Blackberries swing from sweet to sour depending on the season. If yours are tart, add a little more sugar to the filling. If they're already sweet, hold back.Don't overmix the batter. Whisk just until the milk is worked in and the batter is smooth. Overmixing makes the topping dense instead of light.Bake in a 10-ounce ramekin. This is the size I tested the recipe in, and it gives you the right ratio of berries to topping. A dish that's too wide spreads everything thin.If doubling the recipe, double the ingredients and bake in either two 10-ounce ramekins or one 5x5-inch baking dish.