Step 1

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.

Step 2

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.

Step 3

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.

Step 4

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.

Step 5

Warm a medium-sized saucepan to medium heat and add butter. Once the butter has completely melted, allow it to brown, stirring frequently and gently scraping the bottom of the pan with a spatula. The butter will foam and sizzle as brown specks appear on the bottom of the pan.** When the aroma of the pan is nutty and the bottom of the pan is a toasty-brown color remove from heat and let cool completely.

Step 6

Once the butter is completely cooled, beat the butter and sugar together; first on low speed, then increasing as the two ingredients become incorporated. Add the vanilla, salt, and milk, and continue to beat until smooth. If the frosting is still too thick, add more milk, one tablespoon at a time, until the desired consistency is achieved.

Step 7

Once the cake is completely cooled and the frosting is made, assemble your cake. Use a butter knife to loosen the sides of the cake from the springform pan if needed. Remove the parchment paper from the bottom of the cake and place on a cake stand.

Step 8

Frost the sides and top of the cake with a thin layer of frosting using an icing spatula. Set in the refrigerator for 10-15 minutes to allow the base coat or "crumb coat" to set. Take out of the fridge and add remaining frosting, gently scraping the side of the cake with a bench scraper or cake scraper for a clean edge. Using the edge of your icing spatula, create a simple swirl on the top of the cake by gently pressing the spatula into the frosting while turning the cake in a circular motion, moving the spatula from the edge of the cake, slowly toward the center as the cake rotates. This is most easily done with a cake turntable but can be done on a cake stand too.