Preheat oven to 325F Spray the inside of a 10" bundt pan with nonstick cooking spray or butter generously and dust with flour, knocking out the excess. In a small saucepan, heat the root beer, cocoa powder and butter over medium heat until butter is melted. Add sugars and whisk until dissolved. Remove from heat and let cool. In a large bowl, whisk together the flour, baking soda and salt. In a small bowl, whisk the eggs until just beaten. Then whisk the egg mixture into the cocoa mixture until combined. Gently fold the flour mixture into the cocoa mixture. The batter will be slightly lumpy. You can give it a quick whisk if you like, but don't over beat the batter or it could cause the cake to be tough. Don't worry, the batter is very loose (aka thin/runny). Pour the batter into the prepared pan and cook for 35-45 minutes, rotating the pan halfway through the baking. The cake is finished when a sharp knife inserted into the center comes out clean. Transfer to a wire rack to cool completely then loosen edges with a butter knife and turn out onto a cake plate. Spread frosting on top of cooled cake. Slice and serve with vanilla ice cream.
Beat softened butter and cocoa powder. Once combined, add the melted chocolate, salt, powdered sugar and root beer. Beat together until smooth. Spread on top of cooled cake.