Halve the kumquats, blanch in boiling water for 2 minutes, drain and chill in ice cold water. Peel 2 grapefruits and 2 oranges with a sharp knife so that the white skin is completely removed.
Cut out the fillets along the inner thin skins. Squeeze juice out of the parting skins. Squeeze the remaining fruit as well. Fruit pieces and juice must add up to 3/4 litres.
Wash the carambola, cut crosswise into slices of about 1/2 cm thick. Mix the prepared ingredients, cardamom, vanilla pulp and jam sugar in a tall pot. Bring to the boil briefly while stirring, then boil for 4 minutes until bubbly.
Fill into carefully prepared glasses while still hot and seal well with preserving skin.