Step 1To make the espresso granita, dissolve the sugar in the warm espresso. Pour the mixture into a shallow 2-quart glass, plastic or nonreactive-metal pan and place it in the freezer.
Step 2After two hours, remove from the freezer and use a fork to rake any frozen espresso around the edges toward the center. Return the granita to the freezer.
Step 3Continue to scrape the granita every 45 minutes until you get fine crystals. When it's done, you may want to use a metal pastry scraper or spatula to chop the crystals and make them very fine. Store in the freezer for up to two days, until ready to use.
Step 4To make the white chocolate cream, melt the white chocolate with 6 tablespoons of the cream in a medium metal bowl set over a pot of simmering water, stirring until smooth. Remove from the heat and cool to room temperature.
Step 5Whip the remaining cream until it reaches stiff peaks. Fold half of the whipped cream into the melted white chocolate, then fold in the remaining whipped cream. Cover and refrigerate for an hour.
Step 6To serve, spoon the granita into chilled glasses and top with a dollop of the white chocolate cream. Sprinkle 2 teaspoons of chocolate shavings over each. Serve immediately.