In a small bowl, combine rum and Simple Syrup; set aside.
To Assemble the Cake: Cut Chocolate Génoise horizontally into 3 even layers with a serrated bread knife. Place top layer, upside down, on the corrugated cardboard. Brush with rum syrup. Spread a generous ½ cup of Chestnut Buttercream evenly over layer. Brush second cake layer with rum syrup. Place