Preheat oven to 350℉ (175℃).
Whisk flour, baking powder, sugar, and salt in a medium-sized mixing bowl. Set aside.
Place chocolate chunks or chips in a small bowl and microwave in 20-second intervals until melted.
Add cocoa powder, milk, and vanilla extract, and mix until thoroughly combined.
Create a well in the dry ingredients and pour in the chocolate mixture and melted butter. Stir until a thick batter forms.
Pour into a small, ungreased, 8-inch rectangular casserole dish with high sides.
In another bowl, mix cocoa powder, granulated sugar, and brown sugar. Sprinkle evenly over the top of the chocolate batter. PLEASE DO NOT STIR OR MIX.
Gently pour hot water over the mixture. Again, please don't stir. Place a baking sheet in the oven, then put the chocolate cobbler on it in case the batter spills over while baking.
Bake for 30-35 minutes or until the top part sets. Carefully remove it from the oven and cool for 5-10 minutes before serving. Serve warm with vanilla ice cream.