Preheat the oven 325 degrees F. Line two large baking sheets with parchment paper.
Place the nuts in the bowl of a food processor, and process until finely ground or the texture of coarse cornmeal, 10 to 15 seconds. Transfer to a large bowl, and stir in the flour and salt. In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and granulated sugar until light and fluffy, 3 to 6 minutes. Beat in the vanilla, then reduce the speed to low and slowly mix in the flour mixture until combined, about 30 seconds. Roll the dough into balls (about 24 dough balls) and place about 1 1/2-inches apart on the prepared baking sheets. Bake until lightly golden and the bottoms begin to brown, 18 minutes.
Cool the cookies on the baking sheet for 20 minutes. Roll the cookies in the confectioners' sugar just before serving.