Preheat oven to 350 degrees F (180C).
Beat eggs and sugar until creamy.
Add in olive oil, yogurt, lemon juice and grated zest, beat until blended.
Sift together flour and baking powder and gradually combine mixture with wet ingredients beating together until well combined.
Fold in poppy seeds.
Brush a cake pan with melted butter and pour the batter into it.
Bake for 50 minutes or until a toothpick inserted in the cake comes out clean.