In a medium saucepan, combine butter and brown sugar. Cook over medium heat until butter is melted and mixture is smooth; stir frequently. Refrigerate about 15 minutes or until cool.
In large bowl, beat peanut butter and brown sugar mixture at LOW speed until blended. Increase speed and beat 1 minute at HIGH speed. Reduce speed to LOW and add whipped topping. Beat until well blended, about one additional minute.
Pour into crust and refrigerate for several hours before serving.