Preheat oven to 350 degrees. Heat a pot of water on the stove to very hot (just under a simmer).
In the bowl of a stand mixer, combine ¾ cup of the granulated sugar, flour, ¼ cup of the cocoa, baking powder and salt. Stir in milk, melted butter and vanilla and mix until smooth.
Pour the batter into an lightly greased 2-quart ceramic dish (as shown in our photos) or a 9-inch square baking pan (if it’s a non-stick pan, you don’t have to grease it) and spread evenly.
In a small bowl, stir together the remaining ½ cup granulated sugar, brown sugar, remaining ¼ cup cocoa and mix well. Sprinkle this mixture evenly over the batter in your dish or pan. Pour the hot water over the top – but do not stir!
Bake 35-40 minutes if using a glass dish (or 30-35 minutes if using a metal pan) – or until the center is almost set. Remove your dish from the oven and allow it to stand for 15 minutes.
After 15 minutes, spoon the cake into individual serving bowls – making sure to spoon the fudgy sauce from the bottom of the pan over the top of the cake. Add a scoop of vanilla ice cream if desired and serve immediately.