Preheat the oven to 325 degrees F. Lightly butter a 9 inch skillet.
Melt the butter and set aside to cool.
Sift the cocoa powder and flour together and set aside.
In your mixer, beat the eggs and sugar on medium-high speed for 5 to 10 minutes, until very thick and light yellow. After 10 minutes, reduce the speed to low and add the vanilla, coffee extract, and the cocoa powder and flour mixture. Mix very slowly until everything is just combined. Slowly pour in the cooled butter and mix again just until combined.
Pour the mixture into the skillet and place it in a larger baking pan. Add warm water to the pan until it comes halfway up the side of the dish Carefully place it into the oven, making sure not to slosh the water around and bake for 60 minutes.
When it's time to take it out - don't fear - it's absolutely going to look like it's under-baked. (that's normal) Remove the skillet from the water and place in the fridge to cool. Serve in the skillet with ice cream on the side.