Prepare the cake according to package directions in two 9-inch round cake pans.* Line the bottom of the pans with parchment paper rounds for easy removal. Cool completely. At this point the cake layers may be wrapped well and refrigerated for up to two days.
Once the cake layers have been removed from the pans, line one of the clean pans with plastic wrap, leaving plenty of overhang to use as handles later. Spread the softened ice cream in the pan, packing it down and smoothing the surface. Freeze until completely firm. This step may be done several days in advance of the final assembly as well.
To assemble the cake: When the ice cream is very firm, place one of the cooled cake layers face down (flat bottom facing up) on a cake plate.** Using the plastic wrap, remove the ice cream from the pan (if needed, use a dinner knife to pry it loose), peel off the plastic wrap, and center the ice cream on the first cake layer. Place the second cake over the ice cream, rounded side up this time. At this point, I take a knife and spread the ice cream to fill in any gaps and make smooth sides to the cake. Return the cake to the freezer for a few minutes to several hours to ensure the ice cream is firm before icing.
Lastly, ice the cake with the whipped cream, and decorate with sprinkles, cookie, or candy pieces, if desired. Return to the freezer until ready to eat. Once the cake is completely frozen, carefully cover it to avoid drying out.
If the fully assembled cake has been frozen for a few hours, allow it to sit at room temperature for about 5 minutes before slicing with a large, sharp knife. If the cake has been frozen overnight, it will likely need to sit for closer 15 minutes before cutting. The cake layer should be softened enough to cut without enormous effort.