Combine the coffee, sugar, coffee liqueur, and vanilla and stir until the sugar dissolves. Pour the mixture in a flat pan that's about 9 by 13-inches.
Place the pan in the freezer for one hour, until it starts to become slushy around the edges. Rake the mixture with a large fork to break up the crystals and place it back into the freezer.
Every 30 minutes, rake the mixture until it is completely frozen and granular throughout. Freeze until ready to serve.
Spoon the granite into pretty stemmed glasses and top with a dollop of whipped cream. Serve immediately.
For the Sweetened Whipped Cream:
Place the cream, sugar, and vanilla in the bowl of an electric mixer fitted with the whisk attachment. Whip on medium and then high speed until the cream just forms stiff peak.