Step 1: Preheat oven to 350°F and oil a 9-inch round cake pan.
Step 2: Remove zest from all oranges and juice from one. Set fruit aside for another use.
Step 3: In a large mixing bowl with an electric mixer, beat eggs and salt together until frothy and light (about 2 minutes).
Step 4: Slowly add sugar while continuing to mix (about 2 more minutes).
Step 5: Sift the flour and baking soda together and gradually add to egg mixture. Mix about 1 more minute.
Step 6: In a side bowl, mix olive oil, citrus zest and juice. Using a spoon, stir this into the egg mixture, just folding until all inches.
Step 7: Pour batter into prepared pan and place in oven and bake 50 minutes, or until a toothpick inserted in center of cake comes out clean.
Step 8: Cool to room temperature, cut into wedges and serve.
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