Beat peanut butter, vanilla, salt, and melted butter in a medium size bowl until well blended.
In a large bowl, beat together eggs, corn syrup, and sugar. Stir in the peanut butter mixture until thoroughly combined.
Pour filling into unbaked Basic Flaky Pie Crust and bake 10 minutes at 450 degrees F (230 degrees C). Reduce the heat to 325 degrees F (165 degrees C), and continue to bake an additional 35 minutes. Cool.
To Make Caramel Cream: Whip together the cream and the dark brown sugar until stiff peaks form. Chill. Serve with pie.