In a bowl, whisk together flour, granulated sugar, cocoa powder, baking powder, and salt. Add the milk, melted butter, and vanilla extract. Stir until smooth and no lumps remain.
Pour the batter into a greased 9x9-inch baking dish and spread it evenly. In a separate bowl, mix the granulated sugar, brown sugar, and cocoa powder. Sprinkle this dry mix evenly over the batter—don’t stir.
Slowly pour the hot water over the top using the back of a spoon. Do not stir—this creates the gooey sauce underneath.
Bake at 350°F (175°C) for 35–40 minutes. The top should be dry and crackled, with bubbling sauce peeking around the edges.
Let the cobbler sit for 5 minutes so the sauce can thicken slightly. Serve warm with vanilla ice cream or a splash of cream.