Make the Cake: Preheat oven to 350 degrees F. Grease and flour 2 (9-inch) cake pans and line the bottoms with parchment paper.
In a large mixing bowl, cream the butter; then add the sugar and continue mixing until light and fluffy.
Meanwhile, sift together the cake flour, baking powder, and salt.
With the mixer on low speed, gradually add the water and eggs to the butter mixture until blended. Mix in the root beer extract and vanilla. Alternately add the flour mixture and milk to form a smooth batter.
Pour the batter into the prepared pans and bake until just set, about 30 to 40 minutes. Let cool in pans for 5 minutes, and then invert onto cooling racks to cool completely before frosting.
Make the Frosting: In a standing mixer fitted with the whisk attachment, combine the confectioners' sugar and butter. Mix on low speed until well blended; then increase speed to medium and beat for another 3 minutes. Add the cream and vanilla and continue to beat on medium speed for 1 minute more, adding more cream if needed to reach spreading consistency.
To decorate the cake: Place 1 cooled cake layer on a cake stand, frost the top surface, and chill for 15 minutes (or freeze 5 minutes). Place the second cake layer on top, inverting it to create a flat top, and push down on it slightly. Frost the sides and top with a thin layer of frosting to hold in any crumbs (called a crumb layer), and chill 30 minutes or freeze 15 minutes.
Apply a second layer of frosting to finish off the cake, swirling the frosting a bit. Place 12 elbow straws in the cake around the top, and place colored streamers around the edge of the cake flowing down to the base.