Preheat the oven to 350 degrees. Grease an 8 x 8 inch baking pan.or 8 inch cast iron skillet.
In a bowl, whisk together the flour, sugar, 3 Tablespoons of the cocoa powder, baking powder, and salt.
In another bowl, whisk together the coffee extract, vanilla, milk, and butter. Add the butter mixture to the flour mixture and stir to combine. Spread the cake mixture in the prepared pan.
Combine the brown sugar and remaining 4 Tablespoons of cocoa powder. Sprinkle over the cake batter. Spread the chocolate chips over top.
Pour the hot coffee (or water) over top of the cake. Do not stir. Place the pan in the oven and bake for 40 minutes or until the mixture is bubbly with some parts that are set. There will be some molten chocolate parts that will remain liquid. Serve warm with vanilla ice cream.