Preheat oven to 325 degrees Fahrenheit. Generously grease a 9-inch springform pan on the bottom and sides. Line the bottom of the pan with a 9-inch round of parchment paper and grease again. Set aside.
In a stand mixer using the whisk attachment, combine the olive oil and eggs until smooth. Add the milk, lemon juice, lemon zest, orange zest, and sugar and combine again until smooth.
Add the flour, salt, baking powder, and baking soda to the olive oil mixture all at once, and combine, still with your whisk attachment, until ingredients are just barely incorporated. Do not overmix. Remove bowl from stand mixer and use a spatula to scrape the bottom of the bowl and make sure all ingredients are incorporated.
Place the springform pan directly on a cookie sheet, pour the batter into the prepared springform pan, and bake in the oven for 70-80 minutes. The cake will be done when a toothpick inserted in the middle comes out clean or with a few moist crumbs attached. If the toothpick is wet in the center, continue baking for 5-minute increments until done. Allow the cake to cool completely before frosting.
