Place 4 cardamom pods and 1/2 tbsp. ginger in shaker, and muddle until cardamom seeds are separated from husks and ginger is juicy. Add 3 ounces of rum horchata liqueur, 4 ounces of slow-simmered chai and 2 ounces of whole milk with 1 scoop of ice to shaker. Shake vigorously for 10 seconds. Strain into martini glasses in two equal parts. Sprinkle ground cinnamon on top and float star anise to garnish. Repeat process for two more martinis.