Preheat oven to 350 degrees F. Line an 11 x 7 1/2 inch (Brownie) pan with parchment paper.
In a large mixing bowl, combine the cake mix, pudding mix, oil, and 1 egg, with a fork until mixture is crumbly. Reserve 1 cup for later use. Press remaining mixture into the bottom of pan. Bake for 10 minutes. Remove from oven and cool on wire rack.
In a small bowl, beat together with an electric mixer, the cream cheese, vanilla bean paste, 1 egg, and sugar until smooth. Fold in 1/3 cup of the toffee bits. Spread evenly over the cooled crust. Sprinkle remaining crumb mixture over the cream cheese layer. Bake for 15-20 minutes, or until filling is set.
Remove pan from oven the last 5 minutes. Sprinkle butterscotch chips, remaining toffee bits, and white chocolate chips over the top of crumb mixture. Return to oven.
Remove from oven and cool on wire rack 1 hour. Refrigerate for 2 hours, remove from pan by parchment paper and cut into desired size bars.