Preheat your oven to 350°F (175°C).
In a 9x13-inch baking dish, melt the butter.
In a separate bowl, mix together the self-rising flour, granulated sugar, whole milk, vanilla extract, and ground cinnamon. Stir until just combined, taking care not to over-mix.
Pour the batter over the melted butter in the baking dish, without stirring.
Evenly sprinkle the brown sugar over the top of the batter.
Gently pour the hot water over the entire dish, making sure not to stir the ingredients.
Bake in the preheated oven for 30 to 35 minutes, or until the top is golden brown and the cobbler is bubbly around the edges.