How to Make It
Preheat oven to 350°F. Place butter in an 11- x 7-inch baking dish. Place dish in oven (the oven does not need to be fully preheated). Heat until butter melts, about 10 minutes. Remove from oven.
Stir together flour, chocolate chips, 1/2 cup of the brown sugar, 1/3 cup of the granulated sugar, and 2 tablespoons of the cocoa in a medium bowl. Stir together milk and vanilla in a separate bowl. Stir milk mixture into flour mixture until batter is smooth. Pour batter evenly over melted butter in baking dish (do not stir).
Stir together remaining 5 tablespoons cocoa, 1/4 cup brown sugar, and 2/3 cup granulated sugar in a small bowl. Sprinkle evenly over batter in baking dish (do not stir). Gently pour boiling water over mixture in dish (do not stir).
Bake in preheated oven until edges are golden brown and mixture is set on top, 30 to 35 minutes. Serve cobbler warm with vanilla ice cream.