Preheat the oven to 350°F (175°C) and prepare a 9-inch round cake pan with grease and flour.

Wash and cut the whole oranges into quarters, removing any seeds.

Blend the orange quarters in a blender or food processor until smooth, peel included.

In a mixing bowl, beat the eggs and sugar together until light and fluffy.

Stir in the blended oranges, melted butter, and vanilla extract until fully combined.

In another bowl, mix the flour, baking powder, baking soda, and salt.

Gradually stir the dry mixture into the wet mixture until just combined; do not overmix.

Pour the batter into the prepared cake pan, smoothing the top.

Bake in the oven for 40-45 minutes, or until a toothpick comes out clean.

Let the cake rest in the pan for 10 minutes before transferring it to a wire rack to cool completely.

Lightly sift powdered sugar over the top just before serving.