Sieve the flour and put it on a working surface, make a well in the middle and add the sugar, the salt, the grated peel of one lemon and the seeds of half of a vanilla pod.
Pour the egg yolks and the water into your immersion blender container. Put the hand blender to the very bottom of the container, start pouring the olive oil in a thin stream and blend until it thickens into mayonnaise (it is a matter of just a few minutes).
Pour the mayonnaise into the centre of the flour and mix it with the sugar using your fingers to make a soft dough. When it is totally mixed, rub all the ingredients with your fingertips and make crumbles, then start kneading until you have a nice and smooth ball of dough. Roll it out roughly between two foils of parchment paper and place it in the fridge for about 30 minutes.
Heat the oven to 175°Take the shortcrust pastry out of the fridge, unwrap it and roll the dough out to 5 mm thick and cut into desired shapes using cookie cutters. I chose to cut out simple rectangular cookies. Place the cookies on a baking tin lined with previously greased parchment paper. Prick the cookies with a fork.
Bake the cookies for 12 to 15 minutes, until slightly golden. As soon as you remove them from the oven, they are still quite soft, so allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.