In the top of a double boiler combine brown sugar, water, egg white, and cream of tartar or corn syrup. Beat with an electric mixer on low speed for 30 seconds. Place over boiling water (upper pan should not touch water). Cook, beating constantly with the electric mixer on high speed, about 7 minutes or until frosting forms stiff peaks (tips stand straight) and an instant-read thermometer inserted in the mixture registers 160 degrees F. Remove from heat; add vanilla. Beat 2 to 3 minutes more or until frosting is of spreading consistency.