Heat oven to 300 degrees. Toast pistachios in the oven until crisp, about 15 minutes. Do not let them brown. Rub them between your hands to remove as much of the papery skin as possible. Grind the nuts finely in a food processor or nut grinder.

Butter and flour a 10-inch springform pan. Raise the oven to 350 degrees. Sift flour with baking soda, baking powder and salt.

Beat egg yolks with 1/2 cup of the sugar in electric mixer until pale and very thick. Mix in the yogurt and then the olive oil. Fold in flour and nuts.

Beat egg whites with cream of tartar to soft peaks. Add remaining 1/2 cup sugar and beat to firm peaks. Whites should look shiny, not dry and granular. Gently fold egg whites into the batter. Pour into the pan. Bake until cake pulls away from side of pan, about 55 minutes. Cool on a rack.