Prepare an ice-water bath; set aside. Put espresso and sugar into a medium glass bowl; stir until sugar has dissolved. Set an ice-water bath; stir until cooled. Transfer mixture to a 9-by-13-inch glass baking dish; place in freezer. Chill until mixture begins to solidify, about 45 minutes. Remove from freezer; stir with a fork until mixture begins to break up. Freeze, scraping with a fork every 30 minutes, until completely frozen and fine crystals form, about 2 hours total. Whisk cream in a chilled medium bowl until soft peaks form. Divide granita among serving glasses or bowls. Top each serving with a dollop of whipped cream; sprinkle with ground espresso.