Heat oven to 375°F. In medium bowl, beat butter and powdered sugar with electric mixer on medium speed until creamy. Beat in vanilla. On low speed, beat in flour and salt until mixture is crumbly. Stir in 1/2 cup of the walnuts.
Shape dough into walnut-sized balls; roll each into 3x3/4-inch log. Place on ungreased cookie sheets.
Bake 9 to 12 minutes or until set and bottoms are golden brown. Immediately remove from cookie sheets; place on wire racks. Cool completely, about 10 minutes.
Meanwhile, in small microwavable bowl, microwave chocolate on High 30 seconds; stir until smooth.
Place cooled cookies on sheet of waxed paper. Drizzle chocolate over cookies; sprinkle with remaining 1/4 cup walnuts.