In a small saucepan, combine the sugar, cornstarch and butter; stir in milk. Bring to a boil over medium heat; cook and stir for 2 minutes or until thickened. Remove from the heat; stir in vanilla. Cool completely. Stir in condensed milk.
In a large mixing bowl, beat cream until stiff peaks form; fold into milk mixture. Divide between two freezer containers. Stir melted chocolate into one container until well blended. Cover and freeze both mixtures for 6 hours or until firm.
To assemble, place 1/3 cup of ice cream on the bottom of a cookie. Top with another cookie; press down gently. If desired, roll sides of ice cream sandwich in chocolate chips, jimmies, peanuts or coconut. Wrap in plastic wrap. Repeat. Freeze until serving.