Cream butter and sugar. Blend in vanilla, and then blend in flour to form stiff dough.
Divide dough into two gallon-sized plastic food storage bags, roll to ¼-inch thickness and square-off edges with dough scraper, ruler or other straight edge. Chill until firm.
Preheat oven to 350º F.
Cut bag at seams and uncover top of dough. Cut dough with 1¾-inch round or fluted cookie cutter. Dough scrapes can be reformed and placed within the cut bag for rerolling (chill if necessary.)
Place cookies on ungreased cookie sheet. Bake 12-15 minutes or until edges are slightly browned.
Allow cookies to cool. Put about 1½ to 2 teaspoons dulce de leche on flat side of half the cookies, top with plain cookies placed flat side down. Twist cookies to spread filling evenly.
Optional variations: The sides of the cookies can rolled in shredded coconut or cookies can be dipped in or drizzled with melted chocolate, or sprinkled with additional powdered sugar just before serving.
Store in airtight container.