Pierce each kumquat several times with a wooden skewer.
Combine water and sugar in a large saucepan; bring to a boil, stirring until sugar dissolves. Add 3 cloves, 1 cinnamon stick, and 1 star anise. Reduce heat, and simmer 5 minutes. Add kumquats, and simmer 20 minutes or until tender.
Using a slotted spoon, remove the kumquats from pan, and divide evenly between 2 (1-quart) jars. Tuck 3 whole cloves, 1 cinnamon stick, 1 star anise, and half of vanilla bean into each jar.
Bring cooking liquid to a boil; cook 4 minutes. Remove from heat. Strain mixture, discarding solids. Pour 2 cups cooking liquid and 1/2 cup brandy into each jar. Seal jars; shake well. Store in refrigerator 2 weeks before using.