Cut dough into 24 slices, using sharp knife. Bake cookies according to wrapper directions except sprinkle dough with sanding sugar before baking; cool completely before frosting.
While cookies are cooling, make Mint Buttercream Frosting. In medium bowl, mix powdered sugar and butter with spoon or electric mixer on low speed. Stir in mint extract and 1 tablespoon milk. Gradually beat in just enough remaining milk to make frosting smooth and spreadable. If frosting is too thick, beat in more milk, a few drops at a time. If frosting becomes too thin, beat in a small amount of powdered sugar.
To make sandwiches, on each of 12 cookies, top sides down, spread thin layer frosting almost to edge. Top frosting with remaining cookies, top sides up; press together slightly.