To make the cranberry syrup. In a pot, bring 1/2 cup water, the honey, cranberries, ginger, and cardamom to a boil over high heat. Boil 5 minutes or until the cranberries begin to burst, then remove from the heat. Stir in the thyme. Let cool. Remove the ginger, cardamom, and thyme. I prefer to leave the cranberries in, but you can strain those out if desired. Fill a cocktail glass with ice.Combine the vodka, lime juice, pomegranate juice, and cranberry syrup in a cocktail shaker. Fill with ice and shake until combined, about 1 minute. Strain into your prepared glass. Top with ginger beer. Enjoy!