Pour the Jello pudding mix into the Cool Whip. Stir until combined and set aside.
In the bowl of a stand mixer fitted with a paddle attachment, add the cream cheese and mix on medium speed until smooth, about 2 minutes. Add the powdered sugar and mix on low until combined, then increase the speed to medium and mix until light and creamy, about 1-2 minutes.
Add the Cool Whip & Jello pudding mixture into the cream cheese mixture and mix on low until combined, about 1 minute. Fold in the toffee bits.