Lightly grease a 26cm round cake tin. Thinly slice two of the oranges, discarding the end slices. Squeeze the juice from a further two of the oranges, then peel and coarsely chop the remaining orange.
Place the granulated sugar in a large saucepan with 300ml of water. Heat gently stirring until the sugar has dissolved into a syrup and bring to a simmer. Add the orange slices, return to simmering, and simmer gently for 20 minutes.
Once the orange slices are tender, remove with a draining spoon and place in the bottom of the lined cake tin. When cold enough to handle, arrange over the base of the tin and set aside.
Add the orange juice to the pan and bring to the boil. Boil for 10 minutes to reduce slightly, then set aside.
Meanwhile, preheat the oven to 180℃/170℃ fan/gas mark 4. Beat together the butter and caster sugar until light and fluffy, then beat in the egg yolks.
Add the almonds, polenta, yogurt and chopped orange flesh and beat to combine.
Whisk the egg whites until standing in soft peak, then fold into the cake mixture a third at a time. Spoon into the tin and spread level. Bake in the centre the oven for 1 hour until golden and springy to the touch.
While still warm, prick all over with a skewer, then spoon the orange syrup over the cake and allow to soak in. When the cake is cold, transfer to a serving plate and chill until required.
If you use the same beaters that you used to beat the butter and sugar together to whisk the egg whites, make sure you wash them really well in hot water first as any fat on the beaters will prevent the egg whites from whipping up. Polenta is a dish of boiled cornmeal and is an Italian staple. Uncooked polenta is available in packets from any good grocery store, if you can not find it use fine ground cornmeal Freeze: for up to 2 months.