Heat the oven to 176C / 350F. Cover a round cake pan (22 or 23 cm.) with parchment paper and grease.
In a large bowl, using an electric whisk, beat the eggs and sugar for 3 to 5 minutes, or until it triples in volume.
Add olive oil, orange zest and the vanilla. Mix with a spatula.
Sift the 2 flours, baking powder and salt. Add half of the flour to the eggs and mix gently. Add the rest of the flour and mix.
Pour the batter in the prepared pan and bake for 20 to 25 minutes, or until the center of the cake is firm.
While the cake is in the oven, prepare the syrup.
In a small saucepan add all the ingredients for the syrup. Once it starts to boil, lower the heat and boil for 5 minutes. Keep the syrup hot.
Remove the cake from the oven and allow to cool completely. When the cake is cold, pour the hot syrup over the cake.