Prepare an 8" springform pan by spraying with oil (or butter) and lining in parchment paper (sides optional, if you want really clean sides), then spray the paper, too.
Wash and weigh the kumquats (it's really so hard to give a cup measurement for these I recommend using a scale).
Cut the kumquats and remove the seeds. Place them in a food processor or blender until they're in tiny bits. Don't fully purée them.
Place the sugar and eggs in a large bowl and beat with a mixer until light and fluffy.
Sift the flour with the baking powder, then add to the mixture in the bowl a little at a time along with the softened butter. Continue to mix until completely blended, then stir in the yogurt.
Add the processed kumquats to the cake mixture (along with the vanilla if you used baking powder) and stir until evenly combined. Put the batter into the prepared tin.
Bake the Cake:
Bake for 50-60 minutes (depending on your oven), but test with a cake tester or skewer to make sure the orange cake is done before removing from the oven.
Allow to cool for about 15 minutes, then run a thin knife around the perimeter and remove the side of the springform pan.
Make the orange glaze:
Prepare the glaze by melting the sugar in the orange juice and allow to simmer for a few minutes, just until the liquid has a syrupy consistency.
Spoon and brush over the top of the cake and allow to cool completely before cutting.
Serve the kumquat cake:
If desired, you can decorate the cake with some extra kumquats (wash them and the leaves before adding any to the top or sides of the cake).
Slice and serve! Add a scoop of ice cream or freshly whipped cream (without added sugar) for a special treat.
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