1. Split vanilla bean lengthwise; scrape out seeds with a knife tip. Put pod and seeds in a medium saucepan. Add sugar and 1 1/2 cups water and bring to a boil; reduce heat and simmer 5 minutes.
2. Stir in kumquats, return to a simmer, and cook until skins are translucent, about 15 minutes.
3. Strain kumquats over a bowl. Return syrup to pan with vanilla pod and boil until reduced to 1 1/4 cups, 10 to 12 minutes. Stir in kumquats and let the conserva cool.
Make ahead: Up to 2 weeks, chilled.
*To seed kumquats, either thinly slice each kumquat crosswise about a third of the way into the fruit or quarter the fruit lengthwise; then remove seeds with a knife tip.