Preheat the oven to 350° F.
Oil a 9-inch round cake pan.
Remove the zest from the oranges and juice one of them.
Set fruit aside for another use.
Sift the flour and baking soda together onto a piece of waxed paper.
In a large mixing bowl, beat the eggs and salt together with an electric mixer until frothy and light, about 2 minutes.
Slowly add the sugar, continuing to mix 2 minutes longer.
Add the flour and baking soda gradually to the egg mixture, then mix 1 more minute.
In another bowl, combine the olive oil, orange zest, and juice.
Using a spoon, stir it into the egg mixture, folding just until combined
Pour the batter into the prepared pan and bake 50 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Invert onto a wire rack.
Cool to room temperature, cut into wedges, and serve with gelato and a drizzle of new oil or your favorite sweetened fruit sauce.