Preheat the oven to 350 F (177 C). Grease and line the bottom of a 9-inch (23 cm) springform or cake pan with parchment paper.

In a large bowl, whisk together the flour, baking powder, baking soda and salt together until well combined.

In a large mixing bowl fitted with whisk attachment, whisk the sugar and lemon zest together until they are the consistency of wet sand. On low, whisk the eggs and lemon sugar together on low speed until all the eggs are added and combined. Increase the speed to high and whip for 4 - 5 minutes. The egg and sugar mixture will be thick and light yellow in color.

With the mixture on medium speed, stream in the olive oil. Once all the olive oil is streamed in, increase the speed to high for 1 minute. Scrape the sides and bottom of the mixing bowl as needed. On low, whisk in the lemon juice and milk, followed by the dry ingredients. Mix until just incorporated.

Evenly pour the lemon olive oil cake batter into the prepared pan. For a thin, crackle crust, top with granulated sugar.

Bake the olive oil lemon cake for 45 - 50 minutes or until a toothpick inserted into the center of the cake comes out clean or with a few moist crumbs. The crust will be golden brown and the top should bounce back when gently pressed.

Cool the cake in the pan for 10 minutes. Gently release the side of the springform pan and allow the cake to cool for 5 - 10 more minutes. Transfer the lemon cake to a serving plate or serve right from the pan. Top with powdered sugar, slice and enjoy.