One of my favorite textures is that of mochi.  I first discovered mochi ice cream like many others, at the end of a standard Japanese meal.  My preferred flavors were likely to be green tea, red bean, black sesame, or mango.  Mochi can be found in many incarnations other than ice cream: a pancake stuffed with different bean pastes; wrapped around a sweet egg yolk; a ball simply rolled in coconut; another ball floating in a warm black sesame soup, etc. 
Of all the different ways one can eat mochi, I think I like eating it with ice cream best.  The cold gives this rice dough a satisfyingly firm chew, and combined with the creamy chewiness of ice cream, it makes a tasty light workout for the jaw.  The thought of (and my past experience with) wrapping balls of ice cream with sheets of mochi just leaves me wanting to go to the store and buying the boxed version.  I really can't make them better anyway.  My shortcut is the ice cream sandwich.  Pipe ice cream into a puck shaped fleximold and freeze until hard.  Roll the dough and cut out rounds to fit.  Pop out the ice cream and press two rounds of dough firmly around to stick.  Done.  I've done a black and white sesame version here, and it makes a divine afternoon snack.  I'd take this over an ice cream cone anyday.