Stir the sugar into the coffee till dissolved (you can do this over a low heat to speed up the process). Stir in the vanilla and pour into a large rectangular baking dish. Place in the freezer.
After one hour remove from the freezer and use a potato masher to start breaking up any icy chunks that have formed around the edges - use the masher to stir the mixture and return to the freezer. After another hour repeat. At this point the mixture should have an overall slushy texture - if not return to the freezer for about 30 - 45 minutes. Break it up again, give it a stir and freeze for at least 3 hours or overnight.
Use a fork to scrape the granita down the length of the pan, forming icy flakes. Scoop into a bowl and freeze for one hour, or up to one month.
Make the whipped cream:
Beat the heavy cream and sugar till soft peaks form.
To serve, place a few scoops of whipped cream into the bottom of a glass or jar. Top with a few scoops of granita. Repeat, finishing with a dollop of whipped cream. Serve immediately.
Notes
Read this post to learn how to freeze whipped cream!