Halve the kumquats and remove any seeds you find. Place the fruit in a saucepan along with the water and star anise. Boil for about 20 minutes, then add the sugar. Boil for another 20 minutes until the white film has become clear and the liquid has cooked down to a thick syrup. There is not much left now, so keep an eye on it to make sure it does not boil away completely and burn.
Pour into a jar and serve with cheese and biscuits.