Preheat your oven to 180°C (350°F). Prep an 8-inch springform pan by coating it with cooking spray and lining the bottom with a round of parchment paper.
In a large mixing bowl, add the extra-virgin olive oil, room-temperature eggs, granulated sugar, sour cream, fresh lemon zest, lemon juice, vanilla extract, kosher salt, and whole milk.
Whisk vigorously until the mixture is completely smooth and well combined.
Sift the all-purpose flour and baking powder directly into the wet ingredients. Mix with your whisk just until the batter is combined and no dry pockets of flour remain. Do not overmix, or the cake will become dense.
Pour the smooth batter into your prepared springform pan. Bake in the preheated oven for about 45 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean with just a few moist crumbs.
Allow the cake to cool down in the pan for 10 minutes, then transfer it to a wire rack. Once it reaches room temperature, dust the top generously with powdered sugar, slice, and serve!
Notes
Avoid the Bitter Pith: When zesting your lemons, use a microplane and only grate the very top yellow layer of the skin. Avoid the white pith underneath, as it is incredibly bitter and will ruin the cake's flavor.
Weigh Your Flour: Avoid scooping flour directly out of the bag with a measuring cup, which packs it down and causes dry cakes. Fluff your flour with a spoon, scoop it gently into the cup, and level it off with the back of a knife—or better yet, use a digital kitchen scale!
Room Temperature is Mandatory: Cold sour cream and eggs will cause the olive oil to seize up and separate in the bowl. Let your cold ingredients sit on the counter for 30 minutes before starting.
Use a Springform Pan: A nonstick springform pan ensures you can cleanly release the sides of the cake without tearing its delicate, rustic edges.