Whisk nuts and confectioners' sugar in a bowl; reserve 1/2 cup, and set aside. Put yolks and remaining nut mixture into the bowl of an electric mixer fitted with the whisk attachment. Beat on medium-high speed until pale, about 3 minutes; transfer to a large bowl.

Put egg whites and salt into the clean bowl of the electric mixer fitted with the whisk attachment, and beat on medium speed until foamy. Raise speed to medium-high. Gradually add granulated sugar, and beat until stiff peaks form. Beat in the vanilla.

Fold egg whites into yolk mixture in two additions. Whisk flour and remaining nut mixture in a small bowl; fold into egg mixture in two additions.

Transfer half the batter to a pastry bag fitted with a 5/8-inch plain tip (such as Ateco #808). Starting in one corner of a prepared baking sheet, pipe batter in diagonal lines, filling sheet. Repeat with remaining batter in second baking sheet. Bake until pale golden, about 15 minutes. Lift parchment onto wire racks, and let cakes cool completely.