Preheat the oven to 180℃ (160℃ fan/350℉) and line the bottom of a 23 cm (9-inch) round cake tin with parchment paper. Grease the sides well with olive oil.
In a large mixing bowl, use clean hands to massage the lemon zest into the granulated sugar. Set aside while you prepare the dry ingredients.
In a second bowl, whisk together the flour, baking soda, baking powder and salt.
Whisk the eggs into the lemon-infused sugar until just combined. Drizzle in the olive oil, then add the lemon juice and vanilla extract. Whisk everything together until smooth.
Add half the dry ingredients to the wet ingredients and gently whisk. Add half the milk, and repeat. Be careful not to overmix.
Pour the batter into your lined cake tin and firmly tap the tin on the counter a couple of times to knock out any large air bubbles. Bake for 35 to 45 minutes, or until a toothpick inserted into the centre comes out clean. The edges should be a light golden brown and there may be some cracking on top.
Let cool in the tin for 15 minutes. Run a knife around perimeter and release the cake from the tin. Move to a cooling rack and let cool completely.
Dust the cake generously with powdered sugar, and serve with a dollop of chantilly cream. Enjoy!