In a saucepan combine the water and ½ cup sugar and cook while stirring over medium heat, until the sugar is dissolved. Turn the heat up and bring the water to a boil. Cook for about 10 minutes, to create thick syrup. Reduce heat to low.
Slice 2 oranges into very thin slices crosswise, and add them to the saucepan, to cook in the syrup for about 15 minutes. When slices are soft, shiny, and nicely glazed with the syrup, remove them, using a slotted spoon, and place them gently on a tray.
Cut the third orange in half, discard of the seeds, and mash in a food processor (including the peel) to get a smooth puree.
Preheat an oven to 350F. Spray a baking pan with oil, then sprinkle sugar to coat the bottom and sides of the pan. Tap the pan to evenly spread the sugar and shake out leftover sugar.
In a mixer, beat the eggs with oil and sugar for about 5 minutes, until light and fluffy. Add the pureed orange, and eventually the flours.
In the baking pan arrange the orange slices overlapping each other.
Pour the batter on top and bake for about 40-45 minutes. Insert a toothpick into the center of the cake. Cake is ready when the toothpick comes out clean, with just a few tiny crumbs on it.
