Fill a 16-ounce mason jar with ginger root, star anise, peppercorns, cloves, cinnamon stick and vanilla extract. Fill jar with rum. Cover and let infuse for at least 24 hours.
Strain rum through a fine meshed strainer into a bowl. Decant back into jar and replace lid. Spiced rum will keep indefinitely.
In a half-gallon pitcher, combine spiced rum, apple cider and lemon juice. Stir. Serve on the rocks.
Notes
If desired, you can serve this punch with warm apple cider. You can also stretch it with a splash of ginger ale or ginger beer in every glass.