WHISK sugar, cocoa powder, cornstarch and salt in medium saucepan. Gradually whisk in evaporated milk until blended.
COOK over medium heat, stirring constantly, until mixture comes to a boil. Cook 1 minute, stirring constantly. Remove from heat. Add butter and vanilla, stirring until butter is melted. Pour into prepared crust. Cover with plastic wrap, pressing wrap onto surface to prevent skin from forming. Cool completely. Chill 4 hours.
Uncover pie. Spread whipped topping on top of pie. Sprinkle evenly with chocolate curls.