Arrange a rack in the center of the oven; preheat to 350?F. Pour melted butter into the bottom of a 13" x 9" baking dish.

In a large bowl, whisk together flour, brown sugar, baking powder, and salt. Add milk and vanilla, and whisk until combined (a few lumps are okay). Gently spoon the batter over the melted butter, trying not to mix them together.

In a small bowl, whisk granulated sugar and cinnamon together. Evenly pour this mixture over the batter. Slowly pour hot water over the sugar mixture.

Bake the cobbler until it is golden and puffed, about 30 to 35 minutes. Let it cool for 10 minutes before serving with a scoop of vanilla ice cream.