1Heat oven to 375°F. In large bowl, stir cookie mix, butter, flour, eggs and mint extract with spoon until soft dough forms. Divide dough in half. Roll one portion between 2 sheets of waxed paper into 13x10 1/2-inch rectangle. Remove top sheet of waxed paper.
2To remaining half of dough, add food color; mix until uniform in color. Shape into a ball. Roll between 2 sheets of waxed paper into 13x10 1/2-inch rectangle. Remove top sheet of waxed paper; invert colored dough onto plain dough. Peel off top sheet of waxed paper. Trim dough to 11x9-inch rectangle. Tightly roll into a log, starting at long side and using bottom sheet of waxed paper as a guide.
3Roll cookie log in coarse sugar; cut into 1/2-inch slices. On ungreased cookie sheet, place slices 2 inches apart.
4Bake 8 to 10 minutes or until edges are lightly browned. Immediately insert 1 lollipop stick halfway into each cookie. With spatula, carefully remove cookies from cookie sheet to cooling rack. Cool completely, about 20 minutes.