Preheat oven to 350 degrees. Line a 12 count muffin tin with paper liners and set aside.
In a medium bowl, whisk together cake flour, baking powder and salt.
In the bowl of a stand mixer fitted with a paddle attachment, beat sugar and olive oil on medium high speed until light and fluffy, about 2 minutes.
Add eggs, one at a time until well blended. Add vanilla and lemon zest and mix until well combined. With a spatula, add 1/3 of the flour mixture, half the milk, second third of flour mixture, remaining milk and last third of flour mixture. Do not overmix.
Divide the batter evenly among the prepared muffin cups. Bake for 18 minutes or until a toothpick inserted in the middle of the cupcakes comes out clean. Remove from oven and let cool on wire rack. While cupcakes are cooling make frosting.