Heat oven to 325 degrees F and arrange racks in upper and lower third. Combine flour and salt in a medium bowl and whisk until aerated and evenly combined; set aside.
Place butter in the bowl of a stand mixer fitted with the paddle attachment and beat on medium-high speed until light and fluffy, about 3 minutes. Add sugar and vanilla and continue to mix until whipped and light, about 2 more minutes.
Add half of the nuts and mix until evenly incorporated and nuts are broken up, about 1 minute. Add flour and mix until well combined, about 1 minute. Remove bowl from mixer and stir in remaining nuts.
Shape dough into 1 tablespoon balls and place on baking sheets, spaced at least 1 inch apart. Bake, rotating pans halfway through, until underside of cookies are brown, about 25 minutes. Remove from oven and let cool 5 minutes on baking sheets.
Meanwhile, place some powdered sugar in a medium bowl. Once the cookies have cooled, roll them in the powdered sugar until just coated and tap off excess. Let cool completely and recoat in powdered sugar, tapping off excess sugar, before serving.
Recipe courtesy of Aida Mollencamp for 12 Days of Cookies 2008