Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
Wash the oranges and place them in a pot of boiling water. Cook for 15 minutes until soft.
Remove the oranges from the water and let them cool. Once they are cool, cut them into quarters. Remove any seeds and place the oranges in a blender or food processor. Process until smooth.
In a large mixing bowl, beat the eggs and sugar until light and fluffy. Add the vegetable oil and beat until well combined.
In a separate bowl, combine the flour, baking powder, baking soda, and salt. Gradually add the dry ingredients to the egg mixture, mixing well after each addition.
Add the processed oranges to the batter and mix until well combined.
Pour the batter into the prepared cake pan and bake for 50-60 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes. Then, transfer the cake to a wire rack to cool completely.
Once the cake is cooled, you can frost it if desired or serve it as is. Enjoy!