Make the dough: Add all the ingredients for the cookies to a big bowl. Rub the butter with the other ingredients with your fingers, then work it with your palms (you can also use a pastry cutter). The dough will be very crumbly at first, but a minute later or so it will come together. You should have a smooth ball of dough. The dough can also be kneaded with a stand mixer fitted with a paddle attachment - mix at the lowest speed until smooth dough forms. Chill the dough: Divide the dough into 4 parts, roll each part into a log. Wrap each log in plastic foil and put it in the fridge for at least 1 hour (or longer).
Preheat the oven to 350°F (180°C / Gas Mark 4, no fan).
Shape the crescents: Take one log out of the fridge and cut it into 1/2-inch (1 cm) slices. If the dough is cold, shape the cookies with your fingers until they resemble a crescent. If the dough is more warm you can try to roll the slice of the dough between your palms until it forms a cylinder and then bend each end into a crescent shape. Repeat with the remaining dough.
Place the cookies apart (they will spread a little) on a baking tray lined with baking paper. Bake in batches.
Bake the cookies for 10 minutes. They should be pale and only the tips of the crescents should be just lightly golden, the cookies will be completely soft.The baking time is very important - it may vary depending on the oven (every oven bakes a little bit differently). Make sure to not overbake them - they will lose their 'melt-in-your-mouth' feature. While the cookies are baking prepare vanilla sugar: In a food processor, mix powdered sugar and vanilla sugar until very fine. This way you will make powdered vanilla sugar that will stick much better to the cookies than granulated vanilla sugar.You can also just combine powdered sugar with vanilla sugar but I find it doesn´t stick to the cookies as well as powdered vanilla sugar.If you don't have vanilla sugar: scrape out the seeds out of a 1/2 vanilla pod, add to a food processor along with 1/4 cup of sugar, and blitz until well-combined and pulverized. When the cookies are done, transfer them GENTLY with parchment paper to a cooling rack.
Coat the cookies with vanilla sugar: Sprinkle hot cookies with sifted powdered vanilla sugar (when the cookies are cold, the sugar won't stick to them). When the cookies are firm enough to handle take each cookie and dip in vanilla sugar.
Leave the cookies to cool completely.
Enjoy!