Grate 1 tsp. peel and squeeze 3 Tbs. juice from limes. In medium bowl, with mixer at medium speed, beat butter and granulated sugar until creamy. Reduce speed to low; beat in egg and lime peel and juice until blended. Beat in flour until combined. Divide dough in half. On separate sheets of wax paper, shape each half into a 6x2 1/2x1 1/2-inch brick. Wrap each brick in wax paper and freeze 3 hours, or up to 1 month.

Preheat oven to 350 degrees. Slice bricks into 1/4-inch-thick slices. Place slices 1 inch apart on large, ungreased cookie sheet. Bake cookies 12-15 minutes, until edges are golden brown. Transfer to wire racks with a wide spatula. Sift powdered sugar over hot cookies. Repeat with remaining cookie dough and powdered sugar.