In the bowl of a stand mixer, combine softened butter, oil, and sugar.

Using the paddle attachment, whip the mixture for 2 to 3 minutes until light and fluffy.

Add the eggs one at a time, ensuring each is fully incorporated before adding the next.

Mix for an additional 2 minutes on high speed after adding the last egg.

Scrape down the sides of the bowl and sift in the baking powder, salt, and roughly half of all-purpose flour.

Gently fold in the flour until just combined. (You can do this by hand or with the paddle attachment on low speed.)

Add the milk and orange juice, along with a splash of vanilla extract, mixing until fully incorporated.

Mix in the zest of one orange, one lemon, and one lime.

Sift in the remaining flour and fold until just combined.

Prepare a 24cm (9.5in) springform pan by greasing the bottom and lining it with parchment paper.

Assemble the pan, ensuring the parchment is flat against the bottom, and grease the sides.

Pour half of the batter into the prepared pan, smoothing it out evenly.

Bake in a preheated oven at 350°F/175°C for approximately 30 minutes, or until a toothpick inserted into the center comes out clean.

Once baked, release the sides of the springform pan and transfer the cake onto a cooling rack using the parchment paper.

Repeat the process with the remaining batter.