
Preheat oven to 350°F (175°C).
Place ½ cup unsalted butter in a 9x13 inch baking dish; melt in the preheating oven.
In a medium bowl, whisk together 1 ½ cups sugar, 4 tablespoons cocoa powder, 2 cups flour, 2 teaspoons baking powder, and ¼ teaspoon salt.
Gradually add 1 cup milk and 2 teaspoons vanilla extract to the dry ingredients; stir until smooth.
Pour batter over the melted butter in the baking dish; do not stir.
In a separate bowl, mix 2 cups sugar and ½ cup cocoa powder; sprinkle over the batter.
Pour 3 cups boiling water over the sugar and cocoa mixture; do not stir.
Bake for 35-40 minutes until the top is set and cake-like.
Let the cobbler cool for 10-15 minutes to allow the sauce to thicken.
Serve the cobbler warm with a scoop of vanilla ice cream.