I don't really want to purchase an ice cream maker to try this one recipe.  So, is it that necessary?  Is there something else I can do instead?  I made the recipe and have it in a bowl in the freezer.  I am periodically stirring it.  I know it could become a big peach ice cube that I'll be shaving but I just don't want to spend $54 for something I may never use again or have to find a place to store it.  Thanks.

we once made it by putting it in a large can, sealing the can super well and wrapping it in layers of foil.  We then put this in another container and filled it with ice and rock salt.  We let the kids roll it all over the place back ad forth.  after I think about 1/2 hour to 45 mins it was done!!

The process for making ice cream and sorbet is basically the same.  It's the balance between letting it freeze and breaking up the ice crystals without melting them.

Most recipes for granitas (a frozen dessert similar to italian ice) call for doing exactly what you are doing.  Freeze a little, then stir.  Repeat.  Takes 2-3 hours.  The main difference is that with sorbet, like ice cream, you want to mix a little air into the goop.  Try a wisk when you stir.  

Any frozen dessert made this way is best on the day it's made.  They tend to freeze solid when left overnight.

Thanks all.  A granita it is and we love it.