Preheat the oven to 350 degrees Fahrenheit and butter and flour a 9-inch round cake pan.
In a large bowl, whisk the eggs and sugar. Add the olive oil, milk, 1/4 cup orange juice and orange zest and mix well. In a separate bowl, stir the flour, baking powder, baking soda and salt.
Add the dry ingredients to olive oil batter and stir just until smooth. Pour the batter into the prepared pan and bake for 40 to 50 minutes, until a toothpick inserted into the center of the cake comes out clean.
Let the cake cool completely, then turn out onto a plate and dust with powdered sugar.