Preheat the oven to 350°F (175°C).
Pour the melted butter into the bottom of a 9x9 inch glass or ceramic baking dish, ensuring even distribution.
In a large mixing bowl, sift together the flour, 1 cup of sugar, baking powder, and salt.
Incorporate the milk and vanilla extract into the dry ingredients, stirring until a homogenous batter forms.
Spoon the batter evenly over the melted butter in the baking dish; do not stir the layers together.
In a small bowl, whisk together the 1/2 cup of sugar and the ground cinnamon.
Sprinkle the cinnamon-sugar mixture uniformly across the top of the batter.
Slowly pour the boiling water over the entire surface, using the back of a large spoon to diffuse the stream and prevent disturbing the batter layer.
Transfer the dish to the oven and bake for 40 to 45 minutes, or until the top is golden brown and a cake tester inserted into the sponge section comes out clean.
Remove from the oven and allow the cobbler to rest for 10 minutes to set the bottom sauce layer before serving.