Boil the whole oranges until very soft, then cool, halve them, remove any seeds, and blend into a smooth puree.

In a large bowl, whisk the eggs and granulated sugar together until the mixture is light and fluffy.

In a separate bowl, combine the all-purpose flour, baking powder, baking soda, and salt.

Gently fold the dry ingredients into the egg mixture, alternating with the orange puree and vegetable oil, until just combined.

Pour the batter into a greased Bundt pan and bake at 350°F (175°C) for 50-60 minutes, or until a skewer comes out clean.

Allow the cake to cool in the pan for 10-15 minutes before inverting it onto a wire rack to cool completely.

For the glaze, combine powdered sugar and orange juice, then drizzle it over the completely cooled cake before serving.