For the crust: Preheat oven to 350 degrees. Stir together the ground pretzels, melted butter, sugar, and salt. Press the pretzel mixture firmly into the bottom of a 9-inch pie pan. Bake for 10 minutes. Remove from the oven and chill until firm, about 45 minutes to an hour.
For 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. As it's coming to a boil, dip a pastry brush in water and brush down the sides of the pot to remove any sugar stuck to the sides. Cook the sugar mixture, without stirring, until it becomes a rich caramel color, about 10 minutes. Remove from the heat and slowly whisk in the warmed 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.
For the pie: Carefully smooth the warmed peanut butter evenly over the bottom of the pretzel crust. Refrigerate for 10 minutes. Drizzle 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, if necessary. 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.