Step 1 - Prep the blackberries - Preheat the oven to 375°F (190°C). Rinse the blackberries under cool running water and pick out any debris or stems. Transfer the berries to a large mixing bowl and drizzle evenly with lemon juice. Add 1/4 cup of the granulated sugar and 2 tbsp of cornstarch to the berries, and mix gently until they are coated. If using frozen berries, thaw them at room temperature and drain any excess liquid before mixing. - Be patient not to overmix the berries, as their delicate texture can break down easily. Keep them as whole as possible, so they don't release too much juice during baking.
Step 2 - Make the dough - In a separate mixing bowl, combine the all-purpose flour, 1/2 cup of granulated sugar, baking powder, and salt. Add in the 1/2 cup of softened butter and mix with a pastry cutter or a fork to create a crumbly mixture. Pour in the 1/2 cup of whole milk and use a rubber spatula to mix until a soft dough forms. Do not overmix or the crust will become tough. - Work fast to keep the butter from melting and mix it until the largest bits of butter are the size of peas. Use your hands to bring the dough together if needed, but do not knead the dough.
Step 3 - Assemble the cobbler - Grease a 9x13 inch baking dish with butter. Transfer the blackberry mixture into the dish and make sure it is evenly distribute. Take a spoon or your fingers to drop pieces of dough on the top of the berries in a random pattern, within half an inch of each other. Leave gaps in between, to allow the hot berry filling to bubble up and thicken. - If you prefer, you can roll out the dough on a floured surface and then transfer it on top of the berries in one piece, trimming the excess dough that hangs over the edges.
Step 4 - Bake to perfection - Bake the cobbler in the preheated oven for 45-50 minutes, or until the top of the crust is golden brown and crispy, and the berries are bubbling up the sides. Take out of the oven and let it cool for a few minutes before serving. Serve warm with some vanilla ice cream or whipped cream for extra indulgence. - Don't open the oven door too often during baking, as it can release heat and affect the rising of the dough. Take time to gauge the goldenness of the crust and use your nose to sniff the notes of the baked blackberries.