Whip the cream with cream stiffener until firm.
Mix the applesauce with rum to taste: Add just enough rum to achieve the desired flavor.
Cover the bottom of a rectangular baking dish with a layer of sponge cake. Spread a thin layer of whipped cream on top and cover this with a layer of applesauce. Continue layering in this order until all the ingredients are used up (finishing with whipped cream.)
Refrigerate the tiramisu overnight.