Preheat oven to 350°F and line a 9x13-inch pan with parchment paper or spray with non-stick cooking spray.
In the bowl of a stand mixer, fitted with the paddle attachment, or with a hand mixer in a large bowl, beat together the cake mix, chocolate pudding mix, sour cream, oil, eggs, vanilla and water on medium speed until well combined, about 2 minutes. Be sure to scrape the bottom of your bowl as needed.
Coarsely chop the Butterfinger candy bars and fold half of the candy into the cake batter. Reserve the remaining half for topping.
Spoon batter into the prepared pan and use an offset spatula or spoon to spread the batter into an even layer.
Bake in preheated oven for 35-40 minutes, or until the top of the cake springs back when lightly touched.
Allow cake to cool for 10 minutes.
Place peanut butter in a medium microwave-safe bowl. Microwave peanut butter in 15-second increments until warm and drizzly in texture; about 30-40 seconds. Stir in sweetened condensed milk and 3 tablespoons milk. You want this mixture to be smooth and pourable. If it is too thick, gradually add more milk, a little at a time until you reach the desired consistency.
Using a smoothie straw or the handle of a wooden spoon, poke holes across the cake, spaced every inch or so, halfway into the cake.
Immediately pour the peanut butter mixture evenly over the cake, making sure the mixture gets into the holes. Allow cake to cool completely.
Evenly spread the whipped topping onto the cake. Cover and chill for at least 4 hours.
Just before serving, sprinkle the reserved Butterfinger candy bars onto the cake and if desired, drizzle with chocolate fudge sauce.