Combine flour, powdered sugar and cornstarch in medium bowl. Set aside.
Beat butter in large bowl, increasing speed gradually, until creamy. Reduce speed to low and slowly add flour mixture and remaining cookie ingredients. Beat until dough forms (may need to be finished by hand).
Hand roll dough into two 10-inch logs on lightly floured surface. Wrap each log in wax paper and refrigerate for two hours.
Heat oven to 350. Reshape logs if necessary. Cut into ¼ inch slices with sharp knife. Place about 1 inch apart on ungreased cookie sheet. Bake for 9 to 13 minutes or until edges are slightly browned. Cool on cookie sheet 1 minute. Remove from sheet and cool completely.
Meanwhile, prepare glaze. Place powdered sugar in small bowl and slowly add key lime juice for desired glaze consistency. Add key lime peel and stir until mixed. Spoon or brush glaze on cookies. Let stand until glaze in hardened (about 15 minutes).
Store room temperature in sealed container or freeze.