Ditto the Fromage Fort recommendation. I've used this recipe from David Lebovitz with varying cheese mixtures and good results each time. If your cheeses are less interesting, Melissa Clark has a recipe for Jalapeño Fromage Fort in her recent book. The recipe is available online here (scroll down)
Edited to add that I've had only one cheese that completely resisted my efforts to grate it with my mouli-juilenne. It's an old dry jack (Vella Golden Bear) that was rock hard when I bought it and has become like glass over time. I will be trying @andiesenji's steaming method on it very soon! If that fails, it will be joining the Parm rinds in soups!