Preheat the oven to 350°F. Grease and flour a 9-inch cake pan and set aside.
Sift together the flour, baking powder, baking soda, and salt. Set aside.
In the bowl of stand mixer fitted with the paddle attachment, mix together the eggs and sugar until combined. Stream in the olive oil and mix until combined. Add the lemon zest and stir to combine.
Add in half of the dry ingredients and mix to combine. Mix in the yogurt until incorporated. Add the remaining dry ingredients and mix until combined.
Pour the batter into the prepared pan and bake for 28 to 32 minutes, or until a toothpick inserted into the center of the cake comes out clean. Cool on a wire rack for 15 to 20 minutes before removing the cake from the pan. Allow the cake to continue to cool completely before frosting and serving.