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1
Position an oven rack in the center of the oven and preheat the oven to 350u00b0F/180u00b0C/gas 4.
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2
Generously coat the bottom and sides of a 9-in/23-cm round cake pan with baking spray. Line the bottom of the pan with a circle of parchment paper, and coat the parchment with baking spray. Set aside.
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3
Place the eggs, egg yolk, and vanilla in the bowl of your KitchenAid(R) Stand Mixer fitted with the wire whip. Attach the KitchenAid(R) Sifter + Scale Attachment. Close the ingredient valve. Weigh the sugar in the ingredient hopper. Using the whip attachment, turn the mixer on low speed, open the ingredient valve, and sift the sugar into the mixer bowl. Beat the egg mixture on medium-high until it forms soft ribbons and turns light yellow, about 3 minutes. Turn the mixer off.
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4
Close the ingredient valve, and then weigh the flour, baking powder, baking soda, and salt in the ingredient hopper, taring the scale between ingredients. (Keep the hopper closed while you add the yogurt, lemon zest, and olive oil.)
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5
Add the yogurt and lemon zest to the egg mixture in the bowl. Mix on medium-low speed until incorporated. With the mixer on low speed, slowly drizzle in the olive oil until well combined.
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6
With the mixer running, open the ingredient valve, and sift in the flour mixture, just until the flour disappears. Remove the mixer bowl, and use a rubber spatula to blend in any flour remaining on the sides of the bowl.
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7
Using a rubber spatula, spread the batter evenly in the prepared pan. Bake until the cake is deeply golden brown on top, is just starting to pull away from the sides of the pan, and a toothpick inserted into the center of the cake comes out clean, 35 to 40 minutes. For even baking, at the midpoint, rotate the pan from front to back. Place the cake on a wire rack and let cool for 15 minutes. Run a table knife around the inside edge of the pan to loosen the cake. Invert the cake onto a cake plate and peel off the parchment paper. Let cool completely. Dust just the edges, or the entire top with confectioners' sugar before serving. The cake is best when served on the day it is baked. The cake will keep at room temperature for 2 to 3 days in a covered container.
