To make the syrup: In a small heavy saucepan, bring the agave nectar, star anise, ginger and clove to a boil over medium-high heat. Remove from the heat and let cool completely then strain into a small bowl.

To make the cranberry reduction: In a small, heavy, non-aluminum saucepan, bring the cranberry juice to a boil over medium-high heat. Cook for about 7 minutes or until reduced to 1/2 cup. Transfer to a small bowl and let cool completely; the cooled reduction will be quite thick.

Make-Ahead: The ginger-star anise syrup and cranberry reduction can be made 1 week ahead, covered separately and refrigerated; bring the reduction to room temperature before using.

To make the cocktails: In a large glass pitcher, combine the tangerine quarters and mint leaves. Using a muddler or the handle of a long wooden spoon, muddle (mash) the mint and tangerines for 15 seconds. Add the tequila and 3/4 cup of the ginger–star anise syrup and stir well. Fill the pitcher with ice cubes. Stir then add club soda to taste. Pour 1/3 cup of the cranberry reduction over the mixture in the pitcher, pour into ice-filled glasses and serve.