Preheat oven to 340°F/170°C and generously butter and flour a 9-inch or 10-inch springform bundt pan.: Warm air begins the transformation of batter to cake, and the smell of a preheated oven primes your kitchen for baking. Make sure the oven is fully up to temperature before you slide the pan in, because uneven heat can make the cake unevenly risen. I use softened butter to coat the pan, feeling with my fingertips to confirm full coverage, then dust with a light sprinkling of flour so the cake releases cleanly. A common mistake is skimping on the coating, which can cause sticking; be thorough, especially around the pan's crevices.
In a large bowl whisk the eggs and sugar with a hand mixer until pale and fluffy, about 2 minutes.: At this stage you will notice the mixture lighten in color and increase slightly in volume, and the sound of the mixer will change as air becomes incorporated. The pale, ribbonlike batter is a visual cue you have trapped enough air to give the cake lift. Use room temperature eggs if possible, they incorporate more readily. Avoid overbeating beyond the pale and fluffy stage, because too much aeration can cause the cake to collapse later.
Continue to whisk and slowly pour in the extra-virgin olive oil, followed by the milk, then whisk in the vanilla extract and orange zest.: As the thin stream of olive oil enters, the batter will loosen and glisten. You will smell the olive oil's fruity notes marry with the bright citrus from the orange zest . Pour slowly so the batter emulsifies and stays cohesive. If you add the oil too quickly the mixture may separate and lose the trapped air; slow steady pouring preserves structure and yields a silky batter.
Place a sieve over the bowl, add the flour and baking powder and sift the ingredients into the bowl. Whisk all the ingredients gently until just combined, do not over mix.: When the sifted flour falls into the bowl it will create a soft, snowlike dusting. Gently fold with a whisk until you no longer see streaks of flour, stopping early to avoid developing gluten. The batter should look smooth and slightly thickened, not gluey. Overmixing here is the most common error, leading to a tough crumb; stop when things are homogenous and give the batter a quiet rest.
Pour the cake batter into the prepared bundt pan. Place in the oven and bake for about 40 minutes, or until a toothpick inserted in the center comes out clean.: As the cake bakes you will notice the top set and the sides pulling slightly away from the pan. The smell will shift toward caramelized sugar and citrus warmed by the olive oil . Use the toothpick test near the center; if it comes out with a few moist crumbs the cake is done, but if wet batter clings you need more time. Avoid opening the oven repeatedly in the first part of baking, as that can cause the cake to sink in the middle.
Remove the ciambellone from the oven and allow to cool completely at room temperature, then remove from the cake pan. Sprinkle some confectioner's sugar on top if you like and serve.: Cooling is where the crumb sets and moisture redistributes, and the aroma will mellow into a warm, inviting scent. Letting it cool in the pan for a short while helps it firm up slightly, but unmolding too early risks breaking the cake. Once unmolded and fully cooled, the cake accepts a light dusting of confectioner's sugar which highlights the contours. A common slip is forcing removal while still warm, which can tear the crust; patience yields a clean release.