While coffee is hot, stir in sugar until dissolved; add coffee flavored liqueur.
Pour coffee mixture into a 13x9-inch baking dish. Cover tightly with plastic wrap and freeze approximately 45 minutes or until icy at edge of pan.
After 45 minutes, whisk to distribute frozen portions evenly. Cover and freeze again until icy at edge of pan and overall texture is slushy (be sure to scrape the ice crystals off the sides and into the middle of the pan) about 45 minutes.
After 45 minutes, again whisk to distribute frozen portions evenly. Cover and return to freezer and freeze about 3 hours or overnight until frozen solid.
When ready to serve the granita, remove from freezer. Using a fork, scrape granita down length of pan, forming icy flakes. Return to freezer for at least 1 hour. Can be made 1 day ahead. When served, the granita should look like a fluffy pile of dry red crystals.
In a medium bowl, whip whipping cream and 1 teaspoon vanilla extract until soft peaks form. Taste and whisk in more vanilla extract if necessary. Cover and store in refrigerator until ready to serve.
To serve, scoop flaked granita into tall goblets or parfait glasses, filling halfway. Top with prepared whipped cream and sprinkle with shaved chocolate for garnish. Serve immediately with iced tea spoons.
Makes 8 servings.