Prepare Date Filling, and cool completely.
Beat butter at medium speed of an electric mixer until creamy; gradually add sugar, beating until light and fluffy. Add flour, cinnamon, and vanilla, mixing well. Shape dough into a ball. Roll dough to 1/8" thickness on a lightly floured surface; cut with 1 1/2-inch or 2-inch round cutters. Use 1/2-inch cutter to cut out a star in half of cookies. Pierce solid cookies with a fork or wooden pick.
Place cookies on ungreased cookie sheets. Freeze 10 minutes. Bake at 300° for 20 to 25 minutes or until cookies are very lightly browned. Cool 1 minute on cookie sheet; remove to wire racks, and cool completely.
Spread each solid cookie with about 1/2 teaspoon of Date Filling. Top each cookie with a cutout cookie, pressing gently to adhere. Sprinkle with powdered sugar, if desired.