Immediately after brewing the espresso, pour it into a 9×13-inch baking dish, then add the sugar and stir to dissolve. Add the coffee liqueur, vodka, and 2 cups of water. Stir to combine and place in the freezer for 1 hour.
Remove the baking dish from the freezer and mix with a fork to disrupt the forming ice crystals. Return the dish to the freezer for 30 minutes.
Remove the baking dish from the freezer again and, using a fork, scrape the surface to create shards of ice. Repeat three or four more times at 30-minute intervals until the granita has a rough, hardened consistency.
Dollop a few teaspoons of whipped cream into four martini glasses. Spoon the granita on top, then add more whipped cream over the granita. Garnish with a few espresso beans, if desired, and serve immediately. Leftover granita can be stored in the freezer, covered, for up to 1 week. Flake again with a fork before serving.