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1. In bowl beat butter on medium to high speed of electric mixer 30 seconds. Add sugar and salt; beat until combined, scraping bowl. Beat in egg and vanilla. Beat in as much flour as you can; stir in peel and any remaining flour. Cover and chill dough 1 hour or until easy to handle.
2. Preheat oven to 375 degrees F. Lightly grease cookie sheets; set aside. Shape dough in1-inch balls; place 1 inch apart on prepared sheets. Press a thumb in center of each ball. Bake 8 to 10 minutes or until edges are lightly browned. If necessary, repress centers with bowl of teaspoon measure. Cool on racks.
3. Place cherries in cookie centers. Let stand 2 hours. Makes 40 cookies.