Preheat your oven to 350*F and grease your cake pan. Using your mixer, beat eggs and sugar on high until the mixture is fluffy and has doubled in volume (between 5-7 minutes total mixing time). While the eggs and sugar are mixing, in a separate bowl whisk together flour, baking powder, salt and lemon zest. Using a rubber spatula, gently fold in olive oil and lemon juice into the egg mixture. Using the same spatula, fold in flour mixture into the wet mixture until the flour disappears. Do not overmix. Pour the cake batter into your prepared pan and gently tap on a solid surface to remove some of the larger egg bubbles. Bake for 40-45 minutes until the top is a light brown and a toothpick entered in the center comes out clean. Remove from the oven and let cool for 10 minutes. Gently run a butter knife along the edges of the cake to release it from the pan and continue cooling on a wired rack. Dust with powdered icing sugar prior to serving.