Preheat oven to 350 degrees
Grease a 9-in springform pan with oil and line the bottom with parchment paper and grease it as well. Set aside for now
In a large bowl, combine the dry ingredients: both flours, baking powder, lemon zest, and sea salt
In a separate bowl, beat together the egg yolks with half a cup of sugar until well blended on a high speed. Once blended, reduce speed and add olive oil, vanilla extract, and lemon juice, beating until it becomes combined. Slowly add in the dry ingredients and stir using a wooden spoon
In another separate bowl, beat the egg whites with clean beaters until they become foamy and slowly add the remaining ¼ cup of sugar in, beating until peaks start to form.
Fold the egg whites into the cake mixture one at a time, gently folding to mix. Transfer the batter to the springform pan and make sure it is leveled
Bake until golden brown and a toothpick comes out clean when inserted in the center. Let cool for about 10 minutes, then run a knife around the edge before removing pan. Let cool before serving and you remove the parchment paper and bottom of pan. While the cake is baking, before you take it out of the oven, make the syrup
Combine all the syrup ingredients in a saucepan over a medium heat. Stir until it begins to boil then reduce heat to a simmer, all while continuing to stir. Once the sugar has dissolved and the syrup has thickened, slowly pour over the cake while it is cooling. You can also use a brush to spread the syrup on the cake if you don’t want it too syrupy.
Once the cake has finished cooling, cut it in even pieces and serve