In a small saucepan, bring the apple cider, cloves, cinnamon stick and a little bit of nutmeg to a boil. Reduce the heat to medium-low and simmer, stirring occasionally, until the mixture thickens and reduces to 2 oz., about 15 minutes. Strain the cider syrup into a small bowl.
In a cocktail shaker, combine half each of the vodka, Calvados and lemon juice, and 1 oz. cider syrup. Add ice, cover and shake vigorously until cold. Strain into two tall, ice-filled glasses. Top with hard cider. Repeat with remaining ingredients.