Preheat the oven to 350 degrees. Line the bottom of a springform pan with parchment paper and spray the sides with baking spray. Set aside.
Wash the kumquats and slice each one in half. Remove as many seeds as possible.
Place the kumquats in a food processor and process until they are in little bits but not yet pureed.
In a large bowl cream together the butter, sugar, and brown sugar. Mix until light and fluffy.
Add in the eggs and vanilla bean paste and mix until combined.
Mix together the flour, baking powder, and salt in a medium bowl.
Add half the flour mixture to the sugar mixture and mix until combined.
Stir in the vanilla yogurt and mix well.
Add the remaining flour mixture and mix until combined.
Add the processed kumquats to the cake batter and mix until completely combined.
Pour the cake batter into the prepared cake pan.
Bake for 50-60 minutes or until a toothpick inserted into the center comes out clean. Remove from oven and cool for 10 minutes.
Run a butter knife around the edges of the pan and remove the sides of the springform pan. Cool cake completely.
To make the glaze whisk together the juice of one blood orange, the powdered sugar, and the vanilla paste. Whisk until smooth.
Pour the glaze over top of the cake allowing some to drip down the sides.
If desired sprinkle with gold, silver, or clear sanding sugar. Place a few whole kumquats and a couple of mint leaves on top for decoration.