Preheat oven to 350°F.
Butter three 6-inch cake pans. Cut a piece of parchment to fit the bottom of each pan. Butter parchment and flour pans.
Combine milk, olive oil, and orange juice in a medium bowl.
In a small bowl, whisk together flour, baking powder, baking soda, and salt.
Zest orange and set zest aside. Squeeze 1 1/2 tablespoons of juice from orange.
In a large mixing bowl, combine eggs and sugar. Blend with a handheld mixer at medium-high until the mixture is airy and lightens in color, about 10 minutes.
Turn off the mixer and scrape down the bowl.
Alternate adding the wet and dry ingredients. Add 1/3 of the dry ingredients and mix on low just until combined about 30 seconds.
Add half the wet ingredients and continue mixing on low until combined.
Repeat with 1/3 of dry, then 1/2 of wet, finishing with 1/3 of dry ingredients. Mix until just combined.
Stir in zest.
Divide the batter evenly between the three cake pans.
Place in oven and bake for 35–40 minutes. Test the cake for doneness by gently pressing the edge of the cake down; if it springs back and the top is golden brown, it is done. Alternatively, insert a toothpick in the center; if it comes out clean, it is done.
