(Makes about 4 dozen)
2 cups (8 ounces) walnuts (or pecans)
2 cups (10 ounces) unbleached all-purpose flour
¾ teaspoon table salt
2 sticks (16 Tablespoons) unsalted butter, softened
1/3 cup (2.5 ounces) superfine sugar (see NOTE on how to make your own)
1½ teaspoons vanilla extract
1½ cups (6 ounces) confectioners’ sugar (approximate) – for dusting
Adjust oven racks to upper-middle-and lower-middle positions. Preheat oven to 325°F. Line 2 large baking sheets with parchment paper or use silicon mats.
Using a food processor, grind 1 cup of walnuts to coarse cornmeal texture (10 to 15 seconds.) Transfer to medium bowl. Using either the food processor or chopping by hand, coarsely chop the remaining cup of nuts. (5 seconds in food processor.) Transfer to the same bowl and add the flour and salt.
In a large bowl, either using hand mixer or stand mixer, beat the butter and superfine sugar until light and fluffy. Beat in the vanilla extract. With mixer on low, slowly add the flour-nut mixture until combined, about 30 seconds. Scrape the bowl and beaters, then continue to beat on low speed until the dough is cohesive. (About 7 seconds.)
Working with one tablespoon at a time, press and roll dough together into balls and lay on prepared sheets, about 1 inch apart.
Bake cookies until pale gold and the bottoms are just beginning to brown, about 18 minutes, switching and rotating baking sheets halfway through the baking.
Let cookies cook on the cooking sheet for 10 minutes, then move to cooling rack to cool completely, about 1 hour.
Using either a bowl or a paper bag filled with confectioners’ sugar, roll the cookies to coat. Just before serving, re-roll and gently shake off any excess.