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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.