Prepare 2–3 baking sheets by lightly coating them with butter (Residual on the foil butter wrappers is usually the perfect amount and you can just rub the wrappers face-down onto the cookie sheets). Preheat the oven to 375°.

Grind walnuts as fine as possible using a food processor, stopping when it starts to form solid clumps, to avoid over-processing it into nut butter. Add to a large bowl with flour and sugar and stir to combine.

Cut cold butter into small pieces and add to the dry ingredients. Using a pastry cutter (or 2 knives) cut butter into the flour mixture until it forms an even small crumb. (Refer to photo in story for a visual reference.) Use your hands to completely combine the butter into the flour, kneading until the dough forms a smooth ball. Only if needed, add a small amount of milk to help the dough hold together.

Take a small handful of dough and gently roll with light pressure into a log about 1/2" in diameter. Cut roll into 1" pieces. Take each piece and gently roll into the final cookie length, curving into a crescent shape and pinching the ends to taper them. Keep in mind they will puff and grow larger in the oven, so make them a little smaller than your desired final cookie size. Place on prepared baking sheet.

Bake in preheated oven for 15–18 minutes. Rotate the cookies half-way through baking to ensure evenly browned cookies. Check carefully starting at 15 minutes to ensure they don't get too dark—the walnuts are delicate and will go from perfectly golden to burnt in a matter of 30 seconds if you step away! Remove from the oven when the cookies have an even light golden tone. Resist the urge to move the cookies off the sheet, as they are very fragile and will break while too warm. Allow to rest for 5 minutes before moving the cookies to a cooking rack. Allow to cool completely on the rack before coating with vanilla sugar in the next step. 

Mix icing sugar and vanilla sugar in a small bowl, have a small sifter ready. Set out two cookies sheets that fit your cooking rack, and have a metal tin lined with wax or parchment paper ready. Place one cooling rack with cookies into the first cookie sheet. Dust with sugar using the sifter, and also dust the empty cookie sheet beside it. Next, transfer the sugar dusted cookies from the cooling rack to the empty cookie tray you just coated with icing sugar—this is to coat the bottoms of the cookies. Finally transfer the finished cookies into the prepared cookie tin.