Preheat oven to 350°F (175°C).
In a large bowl, combine the chocolate cake mix, butterscotch instant pudding mix, 1 egg, 3 tablespoons peanut butter, and 3 tablespoons canola oil. Mix until the mixture is crumbly. Reserve 1 cup of this crumb mixture for the topping.
Press the remaining crumb mixture evenly into the bottom of an ungreased 9x13-inch baking pan to form the crust. Press firmly so the crust is compact.
Bake the crust for 10 minutes. Remove from oven and transfer the pan to a wire rack to cool completely.
While the crust cools, make the filling: in a medium bowl, beat the softened 8 oz cream cheese, 1/3 cup sugar, and 2 tablespoons sour cream with an electric mixer until smooth and creamy.
Add the remaining 1 egg and 1/2 teaspoon vanilla extract to the cream cheese mixture. Beat on low speed just until combined. Do not overmix.
Fold in the chopped Butterfinger bar (the 1 butterfinger bar, chopped) until evenly distributed. Spread the filling evenly over the cooled crust.
Sprinkle the reserved 1 cup crumb mixture evenly over the filling.
Bake for 15–20 minutes, or until the filling is set (the center should be mostly firm with only a slight jiggle).
Remove the pan from the oven. Immediately sprinkle the top with the 1/4 cup butterscotch chips, 1/4 cup chocolate chips, and the crushed 1/2 Butterfinger candy bar. Return the pan to the oven and bake 1 minute longer to slightly melt the chips.
Remove from oven and cool on a wire rack for 1 hour. Then refrigerate for at least 2 hours or until fully chilled.
Once cold, cut into bars and serve.