Pulse the cookies in a food processor into fine crumbs, then stir in the melted butter until it looks like wet sand. Press firmly into a 9-inch pie plate, up the sides. Chill for 15 minutes while you make the filling.
Beat the cream cheese and peanut butter together until completely smooth with no lumps, about 2 minutes. Add the powdered sugar and vanilla and beat again until fluffy.
In a separate bowl, whip the cold heavy cream to stiff peaks.
Fold about a third of the whipped cream into the peanut butter mixture to lighten it, then gently fold in the rest until no streaks remain.
Spread the filling into the chilled crust and smooth the top. Refrigerate at least 4 hours or overnight until firm. Top with chopped peanuts just before serving.