Preheat the oven to 350F/180C.
Line three 9 inch cake pans with parchment paper.
Mix cake flour, baking powder and salt in a bowl and set aside.
Mix butter, sugar, vanilla and oil in a mixing bowl until light and fluffy.
Add eggs, one at a time, and mix after each adding.
Add in and mix the flour mixture and Greek yogurt in alternation, start and finish with the flour mixture. Mix until just incorporated.
Divide the batter into the three cake pans and bake for 25 minutes or until toothpick inserted in the cake comes out clean or with very few crumbs.
Let the cakes cool completely and then transfer them into different plates.