Prepare pudding mixes according to package directions (using 4 cups milk). Cover and chill for 2 hours. Meanwhile, let cheese stand at room temperature for 30 minutes.
Stir cheese until smooth. Gradually stir 1 cup of the pudding into cheese to lighten it. Fold that mixture into the remaining pudding. Beat whipping cream in a chilled small bowl with an electric mixer on medium speed or with a rotary beater just until soft peaks form. Fold whipped cream into pudding mixture; set aside.
Stir together coffee and the coffee liqueur or hazelnut-flavored syrup in a small bowl; set mixture aside. Shave enough curls from the chocolate to sprinkle over tops of the parfaits; finely chop the remaining chocolate.
To assemble parfaits, arrange half of the ladyfinger pieces in the bottoms of 12 goblets or glasses. Drizzle half of the coffee mixture over ladyfingers in goblets. Spoon half of the pudding mixture on top and sprinkle with chopped chocolate. Repeat with remaining ladyfinger pieces, coffee mixture, and pudding. Top with shaved chocolate curls. Cover and chill about 8 hours or overnight. Garnish each serving with a fresh strawberry, if desired. Makes 12 servings.