Beat butter or margarine in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add the 1/2 cup sugar. Beat until combined, scraping sides of bowl. Beat in egg and vanilla until combined. Beat in as much flour as you can with the mixer. Stir in the remaining flour and the candied cherries with a wooden spoon.
Shape dough into 1-inch balls. Place balls 2 inches apart on an ungreased cookie sheet. Flatten each ball by criss-crossing with the tines of a fork. If desired, sprinkle each cookie with sugar. Bake in a 375 degree F oven about 8 minutes or until edges are golden. Transfer cookies to wire racks and cool.
Spread flat sides of half of the cookies with Cherry Frosting. Top with remaining cookies, flat side down, to form yo-yos. Store in a covered container in the refrigerator. Makes 24 cookies.
Beat cream cheese in a medium mixing bowl until fluffy. Gradually add 1 cup of the powdered sugar, beating well. Add vanilla. Beat in remaining 1 cup powdered sugar to make frosting of spreading consistency. Stir in candied cherries. Makes about 3/4 cup.