Preheat oven to 180ºC (356ºF). Grease with butter a square 9 inch x 9 inch (22cm x 22cm) baking pan then line with parchment paper, allowing the sides to be a bit taller, making it easier to remove the cake once it’s baked. set aside.
First, slice the plums into wedges, set aside.
In a large mixing bowl, add sugar, eggs, and lemon zest.
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.
Arrange sliced plums on top of the batter.
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.
To remove from the pan, gently lift up the sides of the baking paper and transfer cake to a wire rack to cool completely.
Serve and enjoy!