Combine all cookie ingredients in large bowl. Beat at low speed, scraping bowl often, until well mixed.
Divide dough in half. Shape each half into 8x1-inch log. Wrap each in plastic food wrap. Refrigerate 1-2 hours or until firm.
Heat oven to 350°F.
Cut each log into ¼-inch slices with sharp knife. Place 2 inches apart onto ungreased cookie sheet. Bake 8-12 minutes or until set. (Cookies will not brown.) Cool completely.
Combine all frosting ingredients in small bowl. Beat at medium speed, scraping bowl often, until fluffy. Frost cooled cookies.
