Line rimless baking sheets with parchment paper or leave ungreased; set aside.
In food processor, whirl walnut halves with 1/4 cup (50 mL) of the sugar until finely ground.
In large bowl, beat butter until fluffy; stir in nut mixture, then vanilla and salt. Stir in flour, 1 cup (250 mL) at a time. Sprinkle with chocolate chips; stir in. Shape by heaping teaspoonfuls (5 mL) into 1-inch (2.5 cm) balls. Arrange, 2 inches (5 cm) apart, on prepared pans. Cover lightly; chill until firm, about 30 minutes.
Bake in top and bottom thirds of 325?F (160?C) oven, rotating and switching pans halfway through, until bottoms are golden, about 22 minutes. Let rest on pans for about 3 minutes.
Sprinkle remaining icing sugar into shallow wide bowl. Working with about 6 cookies at a time, place, rounded side down, in sugar; roll to coat all sides. Place, right side up, on racks to let cool.
Press icing sugar through sieve to sift. Roll cookies again. (Make-ahead: Layer between waxed paper in airtight container and store at room temperature for up to 1 week or freeze for up to 1 month.)