Preheat Oven & Prepare Pan: Preheat your oven to 356°F (180°C) fan-forced. Grease and line a 9-inch round springform pan with parchment paper. If using a non-stick pan, line the base with parchment paper and grease and dust the sides with flour. Set aside.
Mix Dry Ingredients: In a medium-size mixing bowl, whisk together the flour, baking powder, baking soda and salt. Set aside.
Rub Zest Into Sugar: In a separate large mixing bowl, add the sugar and the lemon zest. Use your fingers to rub the zest into the sugar for 1 minute until the mixture smells fragrant and resembles damp sand.
Beat Eggs Into Sugar: Add the eggs to the sugar mixture and beat using electric hand beaters or a stand mixer on medium speed for 1 minute until pale and slightly thickened.
Add Olive Oil: With the mixer running on low, slowly drizzle in the olive oil to emulsify, taking about 1 minute and 30 seconds seconds in total. Scrape down the sides of the bowl.
Milk, Juice & Vanilla: Pour in the milk, lemon juice and the vanilla. Beat on low for 15 seconds until well combined.
Add Dry Ingredients: Add all of the flour mixture and beat on low speed until just combined and no flour streaks remain. Be careful not to overmix. Use a spatula to gently fold through the batter to ensure everything is evenly incorporated. The batter will be thin.
Bake: Pour the batter into the prepared pan and smooth the top. Bake for 40–45 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Cool: Let the cake cool in the pan for 15 minutes then transfer to a wire rack to cool completely.
Rub Zest into Sugar: In a small bowl, rub ½ teaspoon of finely grated lemon zest into the powdered sugar until fragrant and slightly damp. Dust this lemon-sugar mixture over the cooled cake before serving. Or simply sift over just powdered sugar. Enjoy!