Preheat oven to 350ºF.
Melt butter in a large saucepan over low heat. Add peanut butter and stir until smooth. Mix in sugar and salt; continue to heat until sugars have dissolved. Remove from heat.
Combine eggs, corn syrup, and bourbon in a mixing bowl. Whisk 2 tablespoons of the peanut butter mixture into the eggs until thoroughly combined. Whisk the egg mixture back into the peanut butter mixture; constantly until smooth. Remove from heat and stir in peanuts.
Pour into unbaked pie shell. Bake for 50 to 60 minutes, until center is set. Remove and allow to cool on a wire rack.
Serve with a dollop of whipped cream, if desired.