Preheat oven to 350 degrees Fahrenheit. Line and grease three, six-inch pans, and set aside.

Add eggs and sugar into the bowl of a stand mixer, and beat the the whisk attachment for about 2 minutes.

In a separate medium-sized bowl, combine the wet ingredient (milk, olive oil, lemon zest, and lemon juice).

Combine the remaining dry ingredients (flour, salt, baking soda, baking powder) in another medium sized bowl.

Mix 1/3 of the dry ingredients into the egg mixture on a low speed until just incorporated, then add 1/2 of the wet ingredients. Scrape down the sides of the bowl with a spatula, then repeat this process. Finish by adding in remaining dry ingredients.

Pour the batter evenly between the prepared pans.

Bake for 22-24 minutes, or until a toothpick comes out clean (or with a few moist crumbs). Allow the cakes to cool in the pans for 10 minutes, then flip onto a wire cooling wrack to finish cooling.

Once cooled, level the cake layers using a serrated knife, and assembled the cake.

Cover the outside of the cake with a thin layer of frosting, to create a semi-naked look. Decorate the base of the cake with fresh rosemary sprigs, and place candied lemon sliced to the top of the cake.

Beat the butter and cream cheese on a medium speed for 30 seconds with a paddle attachment, until smooth.

Slowly add in the powdered sugar, 1 cup at a time. Alternate with small splashes of heavy cream and lemon juice.

Once combined, add in the lemon zest and salt, and beat on low until the ingredients are fully incorporated, and the desired consistency is reached.

If the frosting is too thick, add in additional cream (1 teaspoon at a time). If the frosting is too thin, add in more powdered sugar (quarter of a cup at a time).