Preheat the oven to 350 degrees and grease a 9-inch cake pan.

In a medium bowl, whisk the yogurt, sugar, egg and egg yolks together. While continuing to whisk, slowly pour in the melted butter. Continue to whisk until fully incorporated. Add in the flavorless oil and mix just until combined.

Add in the all-purpose flour, cake flour, baking powder, salt, lavender, and lemon zest. Mix until the batter is smooth and glossy. Pour into the prepared baking pan and bake for 30-35 minutes. The cake will be done just before it starts to turn golden, take out of the oven as soon as the top center is set.

Let the cake cool about 10 minutes before turning out onto a cake plate. Mix the glaze ingredients together and brush all around the warm cake. Dust the rest of the cake with powdered sugar.

Serve warm or at room temperature.