Just don't have a cake made of ice cream. I tried that once while I was in the US, and I couldn't finish even 1/8th of it. Not to mention it put me off ice cream for quite a while.
Ice cream cake is awesome!!
Oh and for my previous suggestion, have the ice cream be apple pie flavor and then you'll have pretty much everything you want on one plate!
Or, if you want a different suggestion, Pizookie or red velvet cake. Both are my favorites.