Preheat oven to 350 degrees. Grease a springform pan with olive oil and then line the bottom with parchment paper. I take the sides off and lay a piece of parchment down, then put the sides back on and close the pan. Rub some olive oil on the parchment as well.
In a medium bowl, whisk together the flour and lemon zest. Set aside.
In a stand mixer on high speed, beat the egg yolks and 1/2 cup of the sugar together until pale yellow and thick in texture. 2-3 minutes. Once ready, reduce your mixer speed to medium and add in the olive oil and the 2 tbsp lemon juice and beat until just combined. Then, using a spoon (do not beat) stir in your flour/zest mixture until just combined.
In a separate bowl, add your egg whites and a pinch of salt. Using a hand mixer, mix until foamy. Then, slowly add the remaining 1/4 cup of sugar while mixing. Mix until peak forms.
Fold a third of the egg white mixture into the cake batter and continue folding until you don't see any white. Continue until all egg whites have been added. Pour cake batter into prepared springform pan and sprinkle with 2 tbsp sugar.
Bake for about 40 minutes. Top will be golden and a toothpick should come out clean. Don't let it brown too much. We want it moist! When done, remove from oven and let rest for 10 minutes on a cooling rack. Then remove the sides and let rest for 30 minutes. Finally, gently run the dull side of long knife under the cake to remove it from the pan and parchment paper.
Right before you ice the cake, whisk the powdered sugar, lemon juice and olive oil in a small bowl. To ice, just pour all the icing in the middle of the cake and it will naturally spread out. You can use a small icing knife or the back of a large spoon to help it spread out.