Remove stems and wash fruit with produce wash of your choice. DO NOT PEEL.
Cut in half. Remove seeds if you choose (I didn't and they turned out great).
Bring a water and sugar to boil in a large pot. Boil for 4 minutes.
Add fruit and spices to syrup and boil for 20 minutes on medium/high. Fruit will gradually become more and more translucent, but will not go all the way clear.
Turn off the heat and stir in the vanilla.
Using a fine mesh strainer, seperate fruit from jelly over a bowl. Make sure you save the jelly and don't just pour it down the drain!
Allow both mixtures to cool before scooping them into the lidded jars of your choice.
Notes
If canning, do not strain the kumquats but keep the jelly and fruit combined. Fill pint or half-pint jars and process according to water bath canning directions for 10 minutes.