Remove the vanilla ice cream from the freezer and allow it to soften at room temperature. Line a 9"x2" cake pan with plastic wrap, making sure that you have a fair amount of overhang. Using a spatula, carefully spread the ice cream so that you have a nice even layer. Cover and place in the freezer to firm up, about 2 hours.
Meanwhile, in a saucepan set over medium heat, combine the cocoa powder, sugars, root beer and butter. Heat until the butter has melted. Remove from the heat and add the root beer extract. Allow to cool while preparing the remaining ingredients.
Preheat your oven to 325°F. Line the bottoms of 2 9"x2" cake pans with parchment paper and then lightly coat with baking spray, set aside.
In a large mixing bowl, combine slightly warm butter mixture with the eggs. Mix until the eggs are incorporated. Gradually add the flour, salt and baking soda. The batter will look slightly lumpy but that's ok.
Pour into the prepared pans and bake for 30 minutes. Remove from the oven and allow the cakes to cool in the pans for 30 minutes, then remove them and allow them to cool completely on a wire rack.
Whip the cream along with the powdered sugar, vanilla and salt until it is stiff.
To assemble the cake, place one layer of chocolate cake onto a plate, cake stand, or cake round. Place the ice cream (with plastic wrap removed) onto the top of the cake. Place the other layer on top of the ice cream. Using a spatula, frost the top and sides of the cake with the whipped cream. Garnish with cherries and freeze until you're ready to eat it ?-This chocolate root beer cake is adapted from Baked: New Frontiers in Baking, inspired by Taste & Tell.