Make ahead: 3 days for rice, but assembly at the last minute.
Minimum waiting time: 2 hours
Add the sugar, vanilla, salt and coconut milk to a medium saucepan and bring to a boil while stirring.
Add the rice and continue to boil for two minutes while stirring.
Cover partially and cook over low heat until liquid is almost completely evaporated.
Remove pan from heat and refrigerate two hours to let the rice cool.
Stir a few times.
Meanwhile, boil the fruit infused balsamic vinegar, with the sugar and cinnamon sticks, for about ten minutes while stirring.
Pour this sweet balsamic sauce into a bowl, cover and refrigerate.
Remove the saucepan of rice from the refrigerator. Using the palm of your hand, form the rice into oval shapes, as if to make sushi.
Place them on a large platter and sprinkle with a little ground cardamom.
Cut the fruit into small slices to fit over the ovals of rice.
Serve immediately with the sweet balsamic sauce.