Preheat oven to 350 degrees. Grease a 9x9 baking pan. Set a kettle of water to boil on the stove while preparing the batter.
In a mixing bowl, stir together the flour, sugar, cocoa powder, baking powder, and salt until combined. Whisk in the milk, melted butter, and vanilla extract until a thin batter forms. Don’t worry about a few lumps. Pour the batter into the prepared pan and spread evenly.
In another bowl, stir together the remaining sugar, brown sugar, cocoa powder, and sea salt. Sprinkle the mixture evenly over the cake batter. Gradually pour 1 1/4 cups of boiling water over top of the cake. Do not stir the water in. Allow it to sit on top, undisturbed. Place the pan carefully into the preheated oven. Bake for 35 minutes until the cake is set and the sauce is bubbling. Allow the cake to cool 15 minutes. Scoop the warm cake and sauce into a serving bowl. Top with vanilla ice cream or whipped cream and serve promptly while warm. Cover leftovers and refrigerate. Reheat cake before serving leftovers.