Mix butter, 3 tablespoons corn syrup, and brown sugar together in a saucepan; bring to a boil. Remove from heat and stir in rice cereal. Transfer and press mixture into a 9-inch pie pan. Freeze until firm, 15 to 20 minutes.
Stir peanut butter, 1/4 cup fudge sauce, and 1 teaspoon corn syrup together in a bowl. Spread half the peanut butter mixture onto the crust. Return to freezer until set, 10 to 15 minutes.
Pour the remaining half of peanut butter mixture into the fudge sauce jar; stir well. Refrigerate peanut butter fudge sauce until firm, 10 to 15 minutes.
Spoon and pack ice cream into crust; freeze until firm, 10 to 15 minutes.
Pour peanut butter chocolate sauce into a microwave-safe bowl; heat in microwave until warm, 30 seconds to 1 minute. Serve alongside pie.
