Add the whole Oreo cookies, filling included, to a food processor and pulse until they become fine crumbs. If using a zip-top bag, seal out the air and crush with a rolling pin until no large chunks remain.
Pour the crumbs into a bowl and stir in the melted, slightly cooled butter until every crumb looks damp, like wet sand.
Tip the mixture into the 9x13 dish and press it firmly and evenly across the bottom using the flat base of a measuring cup or your hands. Slide the dish into the refrigerator to firm up while you build the next layer.
In a large bowl, beat the softened cream cheese, creamy peanut butter, and powdered sugar with an electric mixer until completely smooth, scraping the bowl once or twice.
Add 1 cup of the whipped topping and fold it in gently with a silicone spatula until no white streaks remain. Fold in about a third of the chopped Butterfingers for pockets of crunch.
Spread this mixture evenly over the chilled crust with an offset spatula, pushing it all the way to the corners. Return the dish to the fridge.
In a medium bowl, whisk the two packages of instant chocolate pudding mix with the 3 cups of cold milk for about 2 minutes, until it thickens noticeably. Let the pudding sit for 5 minutes to firm up.
Spoon the thickened pudding in dollops over the peanut butter layer, then spread it gently and evenly. Dolloping first keeps you from dragging the peanut butter up into the pudding.
Spread the remaining whipped topping (about 3½ cups) over the pudding in a smooth, even layer. Sprinkle the remaining chopped Butterfingers across the top so every square gets candy.
Cover the dish and chill for at least 4 hours, or overnight, so the layers set firm enough to slice cleanly.