In a small bowl, beat butter, flour and cream. Cover and refrigerate 1 hour or until easy to handle.
Preheat oven to 375°. On a lightly floured surface, roll out dough to ⅛-in. thickness. Cut with a floured 1-¼-in. round cookie cutter. Place 1 in. apart on ungreased baking sheets. Sprinkle with sugar. Prick each cookie 3-4 times with a fork.
Bake 7-9 minutes or until set. Remove to wire racks to cool.
In a small bowl, combine butter, confectioners' sugar, vanilla and enough cream to achieve desired consistency. Remove half to another bowl; tint one portion of filling with red food coloring and the other half with green. Carefully spread filling on bottom of half of the cookies; top with remaining cookies.
