Combine flour and cornstarch. Beat butter and 1 cup sugar in large bowl with mixer until light and fluffy. Gradually add flour mixture, mixing well after each addition. Add nuts; mix just until blended.
Roll dough into 1-inch balls; place, 2 inches apart, on baking sheets. Flatten slightly with bottom of glass.
Bake 13 min. or until centers are set and tops are lightly browned; cool on baking sheets 5 min. Add warm cookies, 1 at a time, to remaining sugar; turn to evenly coat both sides of each. Cool completely on wire racks.