Preheat oven to 350°F. Spread melted butter in a 9x13 baking pan.
Whisk milk, vanilla, and sugar in a large bowl. Add flour, baking powder, salt, and cinnamon; whisk until just combined.
Spoon batter over butter, careful not to mix. Sprinkle brown sugar over batter.
Gently pour hot water over the batter and sugar.
Bake for 30-35 minutes until golden brown and mostly set.
Mix topping sugar and cinnamon; sprinkle over hot cobbler.
Let cool slightly before serving.