Preheat oven to 350 degrees. Line a jelly roll pan with parchment paper, or spray well with nonstick spray.
In a medium or large saucepan, add 1 cup of butter, 1/2 cup of water, 1/2 cup of coffee and 1/2 cup of unsweetened cocoa powder. Bring to a boil over medium high heat. Once it boils, remove mixture from the heat. Let it cool for a minute or two, then stir in brown sugar and 2 teaspoons vanilla. Whisk together until fully combined.
In a separate medium-sized bowl, combine 2 cups of all-purpose flour, 1 cup of granulated sugar, salt, and baking soda. Whisk together to combine dry ingredients. Add your dry ingredients into the sauce pan with the butter mixture. Stir well, then add 1/2 cup of sour cream and eggs. Blend well until all the lumps are gone.
Pour the batter into the prepared pan and spread evenly to the sides. Bake for about 18-20 minutes, or until a toothpick comes out clean. When the cake is done, take it out of the oven and let cool for 15-20 minutes.
While your cake is cooling, make your icing. To a clean, medium-sized saucepan, add 1 stick of butter and 1/4 cup cocoa. Stir together over medium heat until it comes to a boil, then remove from the heat. Add 6 tablespoons of sour cream and 1 teaspoon of vanilla extract. Then use a whisk to stir in the powdered sugar. Spread icing over the cooled cake then serve and enjoy!