In a 13 by 9-inch glass baking dish, carefully pour in hot espresso and whisk in granulated sugar until dissolved completely. Place dish in freezer and every hour, scrape the mixture with a large fork to create the granita texture. The granita will need approximately five hours to completely freeze. The first time you scrape, the granita will not be frozen solid. You want to start scraping while it's still slushy so that texture of the granita will be even throughout.
Right before serving, make the whipped cream. In a large bowl, using an electric mixer with a whisk attachment, beat the heavy cream until soft peaks. Add the vanilla extract and confectioners' sugar and continue to beat until stiff peaks.
Line up 12 glass Champagne flutes. Place 1 tablespoon of granita in the bottom of each glass. Using a different spoon, spread a layer of whipped cream. Continue layering the granita and whipped cream, ending with the whipped cream. Sprinkle chocolate over the top of each glass. Garnish with a sprig of mint. Serve immediately.
Recipe courtesy of Giada De Laurentiis