Boil clementines in a pot of cold water and cook for 2 hours. Drain, and, when cool, cut each clementine in half to remove seeds. Then finely chop the skins, pith and fruit in a food processor.
Beat eggs. Add sugar, almonds and baking powder. Mix well, adding the chopped clementines.
Pour cake mixture into a prepared 9-inch round pan and bake at 375°F for 40-60 minutes.
Slice clementines thinly. Bring granulated sugar and water to a boil in a saucepan. Add clementine slices and let simmer until slices are soft, about 25 minutes. Let cool on a piece of Gefen Parchment Paper.
Sift powdered sugar, add 2 tablespoons clementine juice and mix to a smooth paste. Add more juice if necessary. Pour icing over cake.