Bring the water to a boil, add the vanilla pulp and pod, sugar and kumquats and bring to a boil again. Cover the mixture with a plate (plate should have a smaller circumference than the pot so that it can be placed directly on the kumquats). Let marinate for 24 hours.
Lift kumquats out of syrup, scoop out seeds. Remove vanilla bean as well. Continue to boil down syrup until darker and thicker.
Knead all ingredients for the dough together, wrap in plastic wrap and let rest in the refrigerator for at least half an hour.
Preheat the oven to 190 °C. Grease a tart pan well, spread the kumquats on it so that the whole pan is covered. Drizzle a little syrup over the top. Roll out the dough not too thin and place it on top. Bake for about 20 minutes. Reduce temperature to 170 °C and bake for another 10-15 minutes.
Let the tart cool down. Turn out of the pan and sprinkle with chopped hazelnuts.