Preheat Oven & Prep Pan: Set your oven to 356ºF (180ºC). Line an 8x8 inch square cake pan with parchment paper, ensuring the paper extends over the sides to easily lift out the cake after baking. Set aside.
Prepare Plums: First, slice the plums into wedges, keeping the skin on for added texture and color. Set aside.
Mix Sugar, Eggs & Zest: In a large mixing bowl, use electric hand beaters or a stand mixer with the paddle attachment to beat the sugar, eggs and lemon zest on medium speed for 30 seconds until well combined, scraping down the sides as necessary.
Add Olive Oil: With the mixer running on medium, slowly drizzle in the olive oil in a steady stream, taking about 1 minute, to emulsify.
Incorporate Yogurt and Vanilla: Pour in the yogurt and vanilla, beating for 15 seconds until everything is well combined.
Add Dry Ingredients: Add flour, baking powder, and salt. Mix just until incorporated, about 15 seconds, ensuring not to over-mix to avoid a dense cake.
Transfer Batter: Pour the batter into the prepared pan, smoothing the top with a spatula.
Add Plums: Arrange the sliced plums on top of the batter.
Bake: Place in the oven and bake for 30-35 minutes, or until a toothpick inserted comes out clean or with a few moist crumbs, not wet batter.
Cool: Remove from oven and let the cake cool in the pan for 10 minutes before transferring to a wire rack to cool completely. Enjoy!