Preheat oven to 350°F/180°C. Grease a 12-cup (10-inch) Bundt pan or two standard loaf pans (either 9 x 13 inch pans or 8½ x 4½ inch pans for taller cakes) and set aside.
In a medium bowl whisk together flour and baking powder. Set aside.
In a mixer bowl fitted with whisk attachment, whisk together eggs and sugar on high speed until pale and fluffy, about 5 minutes. On low speed and with the mixer running, add oil slowly until combined. Add orange juice, zest, and vanilla extract and keep whisking slowly until combined. Add flour mixture and whisk just until combined. Don’t overmix.
Pour batter into prepared pan/pans. Bake for 50-60 minutes for the bundt pan or 40-50 minutes for the loaves or until a toothpick inserted into the center of the cake comes out clean. If the top is browning quickly while baking, cover loosely with aluminum foil. Allow cake/cakes to cool completely on a wire rack.
Store cake in an airtight container in the refrigerator for up to 5 days. For the best moist texture, the cake is best served at room temperature. This cake freezes well so if you make two loaves, cover well, and freeze one of them in the freezer for up to 2 months, then thaw overnight in the fridge