Sterilize the jars and lids as per proper procedure.
Wash the kumquats thoroughly. Slice the fruit into thin rounds, removing the stems and seeds as you go. The seeds are full of pectin – bundle them together in cheese cloth and set aside.
Mix together the sliced fruit, sugar, and water in a large bowl and tuck the bundle of seeds in among the mixture. Slice the vanilla bean open, exposing the seeds, and tuck this into the mixture as well.
Cover the bowl with plastic wrap and let it sit at room temperature for 2 hours, or chilled in the refrigerator overnight.
Once the fruit mixture has properly macerated and the juices have thickened, transfer the contents to a non-reactive jam pot or wide skillet (if chilled, allow the mixture to come back to room temperature). Bring the mixture to a hard boil, stirring often to keep the fruit from burning the bottom of the pan. The marmalade will need to boil for 20-30 minutes, until properly gelled at about 220 degrees F.
Remove the pan from heat and discard the seed bundle and the vanilla bean shell (the little black seeds will have distributed throughout the marmalade). Stir in the brandy.
Funnel the marmalade into the prepared jars, leaving ½ inch headspace. Stir to remove any air bubbles, wipe the rims clean with a damp cloth, and apply the lids and rings to finger-tip tightness.
Process the jars in a boiling water bath for 10 minutes, and then let the jars sit overnight to seal. If any don’t seal properly, store in the fridge and eat first.
Due to the high acidity, marmalade has a much longer shelf life when processed properly than other kinds of jams.