Combine sugar, cream, milk, corn syrup and salt in heavy medium saucepan. Bring to boil on medium heat, stirring frequently. Reduce heat to medium-low. Continue cooking, stirring frequently, until mixture reaches 236°F.
Pour mixture into 8-inch square baking pan. Sprinkle with chocolate and vanilla. Leave mixture undisturbed until it reaches 120°F.
Scrape mixture into medium bowl. Stir with a wooden spoon until mixture starts to lighten in color. Stir in OREO Pieces. Continue stirring until mixture thickens.
Spread mixture into parchment paper-lined 8-inch square pan. Let stand several hours until firm. Cut fudge into 36 squares.