Make the Crust: Preheat oven to 350 degrees. Stir together the ground pretzels, melted butter, and sugar. Press the mixture firmly into the bottom and up the sides of a 9-inch pie pan. Bake for 10 minutes. Remove from the oven and chill in the refrigerator until firm, 45 minutes to 1 hour.
Meanwhile, Make the Caramel Sauce. Whisk the sugar, water, and corn syrup in a medium-size heavy saucepan until well combined. Bring to a boil over medium-high heat. Cook the sugar mixture, without stirring, until it becomes a rich caramel color, 5 to 10 minutes. Remove from the heat and slowly whisk in the cream until the caramel sauce is smooth, using caution as the mixture may bubble up. (If the sauce seizes, stir it over low heat until the hardened caramel is melted.) Whisk in the butter and set aside.
Assemble the Pie: Smooth the warmed peanut butter evenly over the bottom of the pretzel crust. Refrigerate for 10 minutes. Pour the caramel sauce over the peanut butter layer and gently spread with the back of a spoon. Sprinkle the chopped peanuts over the caramel layer. Refrigerate for another 10 minutes. Finish with a smooth layer of melted chocolate. Refrigerate the pie until the chocolate is firm, about 30 minutes. Pie can then remain at room temperature until serving. If you have leftovers, cover with plastic wrap and keep at room temperature or in the refrigerator.
*Note: You will not use the entire batch of caramel sauce that you make. You can keep the leftovers in the refrigerator for ice cream topping, apple dipping, or eating with a spoon.