Wash and halve the kumquats, blanch in boiling water for 2 minutes, drain and chill in ice cold. Peel 3-4 oranges with a sharp knife so that the white skin is completely removed.
Cut out the fillets between the parting skins. Press juice out of the parting skins. Orange fillets should yield 300-350 g. Squeeze the remaining oranges. Fruit pieces and juice should add up to 3/4 litres.
Wash the carambola, cut crosswise into slices of about 1/2 cm thick. Mix prepared ingredients, cinnamon stick, star anise and jam sugar in a high pot. Bring to the boil briefly while stirring, then let it boil for 4 minutes until it becomes bubbly.
Fill into carefully prepared glasses while still hot and seal well with preserving skin.