ready in 1 hr 34 min.
You can make vanilla sugar easily at home. Put a few vanilla beans in a jar, and fill with confectioners' or granulated sugar, and let infuse for at least 1 week.
Combine flour, 3/4 cup of the confectioners' sugar, almonds, 2 of the vanilla sugar packets, and salt in a medium bowl. Make a well in the center, add butter and vanilla extract. Using your hands, work flour-nut mixture into butter until the dough reaches a coarse cornmeal-like texture. Sprinkle milk over the dough, knead until smooth, and shape into a ball. Cover with plastic wrap and chill for 1 hour in the refrigerator.
Adjust oven racks to upper and lower-middle positions. Heat oven to 350 degrees F. Line baking sheets with cooking parchment paper. Sift remaining confectioners' sugar and vanilla sugar into a medium bowl and set aside.
Working with about one tablespoon dough at a time, roll and shape cookies into crescent shapes (3/4-inch thick ropes). Bake on lined baking sheets until tops are pale golden and bottoms are just beginning to brown, about 12 to 14 minutes.
Cool cookies on sheets about 3 minutes. Working with three or four cookies at a time, roll cookies in confectioners’ sugar until thoroughly coated. Gently shake off excess. Transfer to a wire rack to cool completely.
Store in an airtight container up to 1 week. Before serving, roll cookies in confectioners’ sugar a second time to ensure a thick coating, and tap off excess.