Preheat oven to 180ºC (356ºF). Line a round 9-inch baking pan with parchment paper, and set aside. NOTE: Alternatively, if you have a non-stick pan, liberally grease it with melted butter and dust it with a light layer of flour. This will leave your finished cake with smooth sides.
In a large mixing bowl, add sugar, eggs, lemon zest, and lemon juice.
Using electric hand beaters, beat on low-medium speed for 30 seconds until well combined. Scrape down the sides if needed with a spatula.
With the beater running on low-medium speed, slowly drizzle in the olive oil in a steady stream to emulsify, about 30 seconds in total.
Add yogurt and vanilla extract, and beat for 15 seconds until well combined. Scrape down the sides if needed.
Add flour, baking powder, and salt. Beat until incorporated, about 15 seconds but do not over-mix, just until it’s incorporated into a smooth batter and no lumps of flour remain. Scrape down the sides.
Pour batter into the prepared baking pan. Smoothing out the top.
Bake for 30-35 minutes, until a toothpick inserted into the middle, comes out clean and it’s lightly golden on top.
Remove from the oven and allow the cake to cool in the pan for 10 minutes.
Transfer to a wire rack to cool.
While the cake is cooling, make the lemon icing.
In a small mixing bowl, combine the icing sugar and lemon juice. Mix with a spoon until well combined and the icing sugar is dissolved.
Take a pastry brush and brush the lemon icing over the cake whilst it’s cooling.
If desired, dust over a light layer of extra icing sugar using a fine mesh sieve.
Serve and enjoy!