Preheat oven to 350 degrees F (175 degrees C). Grease and flour cookie sheets.
Place sesame seeds in small saucepan and stir or shake them over moderate heat until slightly brown. Remove from heat and stir in butter, brown sugar, egg and vanilla. Mix in flour, egg and salt. Drop by teaspoonfuls onto cookie sheets about 2 inches apart.
Bake until just brown, 4 to 6 minutes. Remove from cookie sheets while still warm. If cookies are hard to remove, reheat for 30 seconds.