Wash 2 of the oranges and place in a saucepan with water to cover. Bring to the boil, cover and simmer for 2 hours. Allow the oranges to cool, then cut open, remove the pips and roughly chop the flesh.
Preheat the oven to 190°C. Grease and flour a 22-cm springform tin. Process the cooked oranges, eggs, ground almonds, sugar and baking powder in a food processor.
Pour the batter into the prepared tin. Bake for 1 hour or until the centre is firm (note that this is a very moist cake). Cool in the tin before gently turning out.
Peel the remaining oranges with a small paring knife. Separate the orange segments from the membranes. Serve the cake with the fresh orange segments and some yoghurt on the side.