Let cookie dough stand at room temperature 10 minutes to soften. Meanwhile, heat oven to 350°F.
In large bowl, mix cookie dough, flour and carrots until well blended. Shape dough into 24 balls; place 2 inches apart on ungreased cookie sheets.
Bake 13 to 17 minutes or until golden brown around edges. Cool 1 minute; remove from cookie sheets to cooling racks. Cool completely, about 20 minutes.
In medium bowl, mix filling ingredients until well blended. To make each sandwich cookie, spread about 2 tablespoons filling on bottom of 1 cookie. Top with another cookie, bottom side down. Store between sheets of waxed paper in tightly covered container.