Put the clementines in a pot with cold water to cover, bring to the boil, and cook for 2 hours. Drain and, when cool, cut each clementine in half and remove the seeds. Then finely chop the skins, pith, and fruit in the processor (or by hand, of course).
Preheat the oven to 375°F (190°C).
Butter and line an 8-inch (21 centimeter) springform pan with parchment paper. (I used a 9-inch, it worked fine.)
Beat the eggs. Add the sugar, almonds, and baking powder. Mix well, adding the chopped clementines.
Pour the cake mixture into the prepared pan and bake for 30 to 50 minutes*, when a skewer will come out clean; you might have to cover the cake with foil after about 20 to 30 minutes to stop the top from over-browning.
Remove from the oven and leave to cool, in the pan on a rack.