1. Place a colander in a medium bowl. Line colander with 4 layers of cheesecloth, allowing cheesecloth to extend over outside edges. Spoon yogurt into colander. Refrigerate, uncovered, for 1 hour. Spoon drained yogurt into a bowl; discard liquid.
2. Place whipping cream and sugar in a bowl; beat with a mixer at high speed until stiff peaks form (about 2 minutes). Gently fold whipped cream into yogurt. Refrigerate cream mixture until ready to serve.
3. Spoon 1/2 cup ice cream into each of 8 glasses; top each serving with 2 tablespoons hot espresso and 1 tablespoon liqueur. Top each serving with 2 tablespoons cream mixture; sprinkle each serving evenly with shaved chocolate. Serve immediately.