In a bowl, mix the sugar and the egg.
Add the lemon zest, olive oil, salt and anise. Mix together.
Add the flour. Mix all the ingredients until you get a homogeneous dough. Form a ball, cover it with plastic wrap and let it rest in the refrigerator for at least 1 hour.
Preheat the oven to 180°C (350°F).
On a floured counter, roll out the dough to a thickness of about 2 to 3 mm. Cut out cookies with a cookie cutter (or a knife). Place them on a cookie sheet lined with parchment paper (or a silicone mat). If you have any leftover dough, form a ball and repeat this step.
Sprinkle the cookies with a little sugar and press lightly on their surface to coat it.
Bake for 15 minutes, then let the cookies cool down on a rack.