In a large bowl, whisk together 3/4 cup sugar and the espresso until dissolved. Pour into a 9-by-13-inch metal baking pan; let cool. Freeze, stirring every 30 minutes, until frozen, about 2 hours. Using a fork, scrape into fluffy crystals. Cover and return to the freezer until ready to use.
Meanwhile, using an electric mixer, beat the heavy cream, mascarpone, the remaining 1/4 cup sugar and the vanilla until soft peaks form.
Working in 2 batches, and refrigerating each one, layer each of 8 parfait glasses with 1/3 cup granita, some of the chopped ladyfingers, 1 1/2 teaspoons wine and 1/4 cup mascarpone mixture; repeat. Serve topped with the chocolate shavings.