Combine all ingredients except the anise and put in the fridge covered for 2-6 hours to let flavors develop. Filter the persimmon from the liquid and add star anise and let it infuse for ~5 minutes. Use a ladle to serve in cocktail glasses with ice.
For the allspice simple syrup, add 1 teaspoon of allspice berries into a boiling pot of syrup. (1 cup of sugar, 1 cup of water) Simmer for 30 seconds and then let cool. Sieve out berries and store in refrigerator.