Buy sesame seeds at the health food store, where they're more reasonably priced.
Cook sesame seeds in a heavy skillet over medium heat, stirring often, 5 minutes or until toasted.
Beat butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Stir in sesame seeds, egg, and vanilla.
Combine flour and next 3 ingredients; stir into butter mixture. Cover dough, and chill at least 1 hour.
Shape dough into 1/2-inch balls; place on a lightly greased baking sheet. Flatten to a 1/16-inch thickness with floured fingers or a flat-bottomed glass.
Bake at 325° for 8 to 10 minutes or until lightly browned. Transfer to wire racks to cool.
Tip: Pressing dough into a teaspoon measuring spoon creates about a 1/2-inch ball.
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