In a small saucepan combine the sugar and espresso over medium heat. Stir until the sugar dissolves, about 5 minutes. Place the chocolate in a small bowl. Pour the sugar and espresso mixture over the chocolate and let sit until the chocolate melts, about 3 minutes. Add the coffee liqueur and stir to combine. Place the chocolate mixture in the freezer for 10 minutes to cool.
Place the chocolate mixture in a pitcher and add the Prosecco. Gently stir to combine. Pour into chilled glasses and serve.