Pour hot, freshly brewed coffee into a large metal or freezer proof glass pan (13" x 9" or slightly larger) that will fit in your freezer. Add sugar to hot coffee and stir until sugar has dissolved. Allow mixture to cool to room temperature.
Once mixture has cooled, carefully move pan to freezer. Check after about 45 minutes and when edges are just beginning to freeze, give it a stir with a fork and place it back in the freezer. Continue this process about once every half hour, scraping with the fork until mixture resembles shaved ice and no liquid remains at bottom of pan. This will take approximately 3 hours or more.
Place a small metal mixing bowl in the freezer for about 30 minutes. In the chilled bowl, whip the heavy cream and vanilla with a hand mixer. Add 1 tablespoon sugar until soft peaks form.
Layer granita alternately with layers of whipped cream into parfait or other serving glasses.