Preheat the oven to 350° FGrease and flour a Bundt or tube cake pan. Wash and zest the oranges, then juice them. Using an electric mixer, beat the eggs and sugar in a large bowl until pale and thick. Add the oil gradually and beat until well combined.
Combine the flour, baking powder, and salt in a separate medium bowl. Add it to the eggs and sugar mixture and stir lightly to combine.
Pour in the orange juice and beat until smooth. Mix in the vanilla and orange zest.
Pour the batter into the prepared cake pan. Bake in the oven for approximately 40 minutes, or until the sides of the cake pull away from the pan and the cake tests done. You can test by inserting a toothpick into the center. If it comes out dry, your cake is done
Take the cake out of the oven and let it cool for 7 to 10 minutes. Carefully remove the cake from the pan and place it on a rack to finish cooling.
Leave as is or once cooled dust with powdered sugar. Or make a quick glaze with a ¼ cup powdered sugar and a tablespoon or two of the freshly squeezed orange juice.