Poking holes in the dough allows steam to escape, helping to give this walnut shortbread its crisp texture.
Preheat oven to 325 degrees. Pulse walnuts in a food processor until finely ground. Transfer to a bowl, and whisk in flour and salt.
Beat butter, sugar, and vanilla until pale and fluffy. Slowly add walnut mixture, and beat until just combined.
Butter an 8-inch round cake pan. Transfer dough to pan. Place a piece of plastic wrap on dough, and use it to press the dough evenly into pan (this will prevent the dough from sticking to your fingers). Cut dough into 8 wedges using a paring knife. Prick all over with a wooden skewer or fork.
Bake until golden brown and firm in center, 30 to 35 minutes. Transfer pan to a wire rack. Recut into wedges and prick again. Let cool slightly. Dust with confectioners' sugar.