Mix all the liquid ingredients - the olive oil, citrus juice and grated zests and vanilla, and beat them together with the sugar.
Stir constantly until you get a solid but softer than biscuit dough. Cut thus prepared dough into cookies using shapes, spray them out using a pastry bag or simply shape them into balls with your hands.
Arrange the orange cookies in a tray with baking paper and put to bake for 10-12 minutes in a preheated 392°F (200 °C) oven until pinking. Let the ready orange cookies cool for a few minutes on the paper before you remove them.