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Mix flour, cream of tartar, baking soda and salt in medium bowl. Set aside. Beat butter in large bowl with electric mixer on medium speed until light and fluffy. Add sugar; beat until well blended, scraping sides of bowl occasionally. Beat in eggs and vanilla. Gradually beat in flour mixture and 1/4 cup of the toasted sesame seed on low speed until well mixed
Refrigerate dough 2 hours or until firm
Preheat oven to 400°F. Shape dough into 1-inch balls. Roll in remaining 3/4 cup toasted sesame seed. Place 2 inches apart on ungreased baking sheets
Bake 6 to 8 minutes or until lightly browned. Cool on baking sheets 1 minute. Remove to wire racks; cool completely. Drizzle cookies with melted chocolate. Let stand until chocolate is set