Preheat the oven to 350 degrees and grease a 9-inch round cake pan with olive oil.
In a small bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, stir together the eggs, 1 cup of the coconut sugar, olive oil, orange juice, vanilla extract, and orange zest. I like to use a microplane to zest the orange very finely.
Add the dry ingredients to the wet ingredients and stir just to combine.
In the greased pan, place thin slices of oranges on the bottom of the pan and sprinkle with the remaining 1/4 cup of coconut sugar. (Optional: Remove the peel from the orange before slicing if the skin is quite thick.) Pour the batter on top of the orange slices.
Bake the cake for 40 to 45 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan on a wire rack for a few minutes, then carefully remove it from the pan to the cooling rack.