Preheat the oven to 180C/gas mark 4. Butter a 26cm, round springform tin and dust with flour.
Chop the pistachio nuts finely in a food processor.
Sift the flour with the bicarbonate of soda, baking powder and salt. Add the orange zest.
Beat the egg yolks with half the sugar until pale and thick. Mix in the yoghurt and olive oil, then fold in the chopped pistachios and flour.
Beat the egg whites with the cream of tartar until they hold soft peaks. Add the remaining sugar and beat until they hold stiff peaks. Fold into the cake mix. Pour into the tin. Bake for 45 minutes. Cool in the tin. This is good served when still slightly warm, with poached apricots, but you can bake it a day in advance.