Beat butter with sugar, gradually adding the eggs and vanilla. Add the yogurt and continue beating until you get a well blended mixture.
Mix the baking soda with the flour. Pour the flour into the yogurt mixture and beat it until you come up with a soft dough.
Brush with butter a medium-size baking dish. Spread the cake dough inside and bake at 170-180° C for 40-45'. Let the yogurt pie cool, before cutting.