Heat the oven to 175 C / 350 F. Lightly butter a 15 cm / 6-inch square baking dish.
In a mixing bowl, whisk together the flour, granulated sugar, 15 g cocoa powder, baking powder, and salt.
Add the milk, melted butter, and vanilla. Stir until you have a smooth, lump-free batter.
Pour the batter into the prepared dish and spread it evenly to the edges with a spoon.
In a small bowl, stir together the brown sugar and remaining 15 g cocoa powder. Sprinkle it evenly over the batter, but don't stir it in.
Pour the hot water gently and evenly over the top, over the back of a spoon so it doesn't dig craters. Do not stir.
Bake for 26 to 30 minutes, until the top looks set like a cake and springs back lightly, with sauce visibly bubbling at the edges. The center should still wobble a little when you nudge the dish.
Let the cobbler cool on a rack for 5 minutes. The sauce thickens slightly as it sits, so don't wait too long.
Spoon into bowls, scooping sauce up from the bottom of the dish over each portion. Serve warm, with ice cream if you like.