Preheat oven to 350 degrees
Mix flour, baking powder, and lemon zest in a bowl.
In a separate bowl beat olive oil, yogurt and sugar for 10 minutes
Beat egg yolks in a separate small bowl
Add egg yolks to oil mixture, folding in until the mixture is smooth. Add flour and mix well by hand.
Brush baking dish with olive oil. Add cake batter and bake for 1 hour.
Brush cake with melted butter, honey, and balsamic mixture.