Preheat an oven to 350°F. Cream the butter and ½ c. of the powdered sugar at low speed. Beat in the vanilla. Then gradually add the flour and chopped nuts. Mix until the dough is no longer sticky.
Dust your hands with flour and roll the dough into balls, about the size of golf balls. Use the bottom or side of a cup to flatten each ball to a ¼-inch disc. Then use the top of the cup to cut each disc into a crescent shape.
Place the cookies on a baking sheet lined with parchment paper. Leave a couple of inches between each cookie. Bake 12-15 minutes, or until the edges look crisp. Remove from oven and let cool about 5 minutes.
Put the remaining 1 c. powdered sugar in a bowl. Dip each cookie into the powdered sugar while still warm. Enjoy the cookies when they’re cool enough. You can also store them in an air-tight container after they cool completely.