Place the butter in an 11x7-inch baking dish (or similar size such as 8x8 square, I used a 1 1/2-quart round dish). Place the dish in the oven until the butter melts completely, about 5-7 minutes. Remove from the oven.
In a medium bowl, stir together the flour, chocolate chips, 1/2 cup (105 g) of the brown sugar, 1/3 cup (65g) of the granulated sugar, and 2 tablespoons (30g) of the cocoa. In a separate measuring pitcher with a pour spout, combine the milk and vanilla; mix well. Pour the wet ingredients into the dry and stir until batter forms with no streaks of flour remaining.
Dollop the batter over the melted butter in the pan but do not stir. The batter will sink and the butter will pool to the top.
In a medium bowl, stir together the remaining 5 tablespoons (37.5 g) of cocoa, 1/4 cup (55g) of brown sugar, and 2/3 cup (135g) of granulated sugar. Whisk to combine. Sprinkle evenly over the batter in the baking dish. Do not stir.
Gently pour the boiling water over the layered mixture in the pan. Do not stir.
Bake for 35-40 minutes or until the crust is formed and set on top. Cobbler may jiggle a little when removed from the oven, this is normal. Let cool slightly before portioning warm cobbler to dishes; top with scoops of vanilla ice cream.
Cover leftovers and store in the refrigerator. Re-warm bowls of cobbler in the microwave, or reheat ramekins of cobbler in a preheated oven for 10 minutes.
If you don't have salted butter, add a pinch of salt to the batter.If you don’t have self-rising flour on hand, combine 1 cup of all-purpose flour, 1 1/2 teaspoons of baking powder and 1/4 teaspoon salt in a small bowl. Whisk to combine. Use in place of self-rising flour in this recipe.