root beer bundt cake
as seen on vanillasugarblog.com
From Baked: New Frontiers in Baking 

Cake:
1 1/2 cups root beer (do not use diet root beer)
1/2 cup root beer schnapps (if you cannot find schnapps then use 2 cups of root beer soda instead of the 1 and 1/2 cups as stated above)
1 cup dark unsweetened cocoa powder
½ cup (1 stick) unsalted butter, cut into 1-inch pieces
1¼ cups granulated sugar
½ cup firmly packed dark brown sugar
2 cups all-purpose flour
1¼ teaspoons baking soda
1 teaspoon salt
2 large eggs

Frosting:
2 ounces dark chocolate (60% cacao), melted and cooled slightly
½ cup (1 stick) unsalted butter, softened
1 teaspoon salt
¼ cup root beer OR 1/8 cup of root beer schnapps
2/3 cup dark unsweetened cocoa powder
2½ cups confectioners' sugar

For a more prominent root beer taste it is advised to use root beer schnapps.  If you do so, then use 1 and 1/2 cups of root beer soda AND 1/2 cup of root beer schnapps.

Preheat the oven to 325 degrees F. Generously spray the inside of a 10-inch bundt pan with nonstick cooking spray; alternatively, butter it, dust with flour, and knock out excess flour.
In a small saucepan, heat the root beer, cocoa powder, and butter over medium heat until the butter is melted. Add the sugars and whisk until dissolved. Remove from heat and let cool.
In a large bowl, whisk the flour, baking soda, and salt together.
In a small bowl, whisk the eggs until just beaten, then whisk them into a cooled cocoa mixture until combined. Gently fold the flour mixture into the cocoa mixture. The batter will be slightly lumpy - do not overbeat, as it could cause the cake to be tough.
Pour the batter into the prepared pan and bake for 35 to 40 minutes, rotating the pan halfway through the baking time, until a small sharp knife inserted into the cake comes out clean. Transfer the pan to a wire rack to cool completely. Gently loosen the sides of the cake from the pan and turn it out onto the rack.

For the root beer fudge frosting:
Put all the ingredients in a food processor. Pulse in short bursts until the frosting is shiny and smooth. Use a spatula to spread the fudge frosting over the crown of the bundt in a thick layer. Let the frosting set before serving.