Toss together first 4 ingredients in a large bowl. Stir raisins into carrot mixture.
Tear cookie dough into pieces, and stir into carrot mixture until well combined.
Drop cookie dough mixture by tablespoonfuls, 2 inches apart, onto lightly greased baking sheets. (Dough should make 24 cookies.)
Bake at 350° for 15 to 18 minutes or until edges are crisp. Cool on baking sheets 5 minutes. Remove to wire racks, and cool 10 minutes or until completely cool.
Turn half of cookies over, bottom sides up. Spread each with 1 Tbsp. chilled Cream Cheese Icing. Top with remaining cookies, bottom sides down, and press gently to spread filling to edges of cookies.
Note: For testing purposes only, we used Pillsbury Create 'n Bake Sugar refrigerated cookie dough.
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