Whisk together the sugar and 1/4 cup cream in a medium bowl. Whisk until the cream forms soft peaks, then whisk in the vanilla and set aside.
Put the coffee in a small saucepan over low heat until just simmering. Stir in the remaining 1/2 cup cream and heat through, about 1 minute. Stir in the coffee liqueur and vodka. Pour into 2 big coffee mugs, then top with the whipped cream and serve.