Combine milk, cinnamon sticks and whole cloves in medium saucepan. Bring to a simmer. Remove from heat. Add both chocolates and whisk until melted. Cover and let stand 15 minutes to allow flavors to blend. Bring milk mixture to simmer. Add coffee, 2 tablespoons sugar and 1 teaspoon vanilla; stir over medium-low heat until flavors blend (do not boil), about 5 minutes.
Meanwhile, beat cream, pinch of nutmeg, 1 tablespoon sugar and 1/2 teaspoon vanilla in small bowl until soft peaks form.
Strain cappuccino; ladle into mugs. Top with cream. Sprinkle with more nutmeg.