In a saucepan, combine the sugar, cornstarch, milk, butter, and salt.
Place pan over medium heat and cook, stirring or whisking continuously for 5-7 minutes or until the mixture starts to boil.
Lower heat slightly and continue to cook, rapidly whisking for about 2 minutes.
Remove pan from heat and stir in vanilla.
Pour the filling into the cooled pie shell, smooth the top.
Place the pie on a wire rack; let cool completely, then refrigerate at least 2 hours or overnight.
Serve with a dollop of whipped cream.