Grease a 22cm (8½inch) spring-form cake tin and line the base with baking paper.
Scrub the orange skins under warm running water with a soft bristle brush to remove the wax coating. Put the whole oranges in a saucepan, cover with water and boil for 1 hour. Remove from the water and set aside to cool.
Preheat the oven to 180°C (350°F/Gas 4). Using a plate to catch any juice, cut the cooked oranges into quarters and remove any seeds. Put the orange quarters, including the skin, into a food processor or blender and process until the oranges turn to a pulp.
Beat the eggs in a large bowl with electric beaters until light and creamy. Add the orange pulp and any reserved juice, the ground almonds, sugar and baking powder to the bowl. Mix thoroughly, then pour into the prepared tin.
Bake for 1 hour, or until the cake is firm to touch and lightly golden. Cook the cake a little longer if it is still wet. Leave in the tin for 10 minutes, then remove from the tin and leave to cool completely. Dust with sifted icing sugar and serve with cream.