Preheat the oven at 175ºC/ 350ºF.
Start by browning the butter over medium in the skillet you'll be baking the cake in. If you don't have a skillet, brown the butter in a pan and bake the cake in baking pan or baking dish. Pour the brown butter into a bowl to slightly cool, while preparing the rest of the cake.
In a bowl stir together the all-purpose flour, cocoa powder, granulated sugar, dark brown sugar, espresso powder, baking powder and salt with a whisk.
Then add the milk, vanilla extract and browned butter. Stir the cake batter together until smooth and combined.
Add the cake batter into the skillet.
Then in a small bowl, mix together the granulated sugar, dark brown sugar and cocoa powder. Sprinkle it over the cake batter.
Lastly gently pour boiling water over the back of a spoon, so the water gently spreads over the cake.
Bake for 30-35 minutes. Let it rest for 15 minutes before serving with vanilla ice cream.
