Preheat oven to 350 degrees and lightly grease a 9 x 13-inch pan.: You should notice the kitchen warming as the oven reaches 350 degrees , and a faint metallic hum from the preheat is normal. Greasing the pan ensures the bars release cleanly, and the light shimmer of oil or spray on the pan surface is a good visual cue. If the pan is not well greased the crust can stick, so take a moment to cover corners thoroughly. A common mistake is under greasing, which causes tearing when you lift the bars out.
In a large bowl, use a hand-held mixer to mix yellow cake mix, butterscotch pudding mix, oil, and 1 egg until mixture is crumbly. Set 1 cup of mixture aside and press remaining mixture into the bottom of the prepared pan. Note: Just use the dry pudding mix. Do not add any milk.: Just use the dry pudding mix. Do not add any milk. : As you blend the dry yellow cake mix and dry butterscotch pudding mix with vegetable oil and 1 egg , you will hear the mixer shift from a loose powder to a coarse, sandy texture, with small clumps forming. The aroma will carry a concentrated sweet and vanilla like smell from the cake mix and butterscotch. When you press the remaining mixture into the pan, you should feel it pack firmly but not soggy, creating an even layer. Reserving exactly 1 cup gives you a crumb topping with similar flavor and texture. If you overmix into a paste the crust will be dense, so stop when it becomes crumbly.
Bake for 10 minutes and then cool.: During the 10 minutes in the oven you will notice the crust set and the edges begin to take on light golden notes. The kitchen will fill with a toasty, sweet scent. After removing from the oven let it cool until it is warm to the touch, not piping hot, so the filling does not melt into the crust. Cooling also firms the base, which helps the filling stay distinct. A common mistake is trying to add filling while the crust is too hot, which can cause the layers to blend and a soggy texture.
Beat cream cheese and sugar until smooth and creamy. Beat in remaining egg. Stir in 1/2 cup toffee bits. Spread mixture over crust. Sprinkle with the 1 cup of set aside crumb mixture.: When you beat the softened cream cheese with sugar , the motion should transform a slightly chalky block into a glossy, silky mass. You will see the mixture lighten in color and the graininess disappear, and the sound of the mixer will change to a smooth whirl. Adding the second egg loosens the mixture and helps it spread easily. Folding in 1/2 cup of brickle toffee bits introduces nutty crunch, and you should distribute them evenly so every bite has texture. When you spread the filling over the warm but not hot crust, use a rubber spatula to achieve a smooth surface. Finish by sprinkling the reserved crumb evenly for a rustic top. Avoid overbeating the filling, which traps air and can cause cracks during baking.
Bake 15 to 20 minutes or until filling is set.: As the bars bake the filling will puff slightly and then settle; listen for a gentle silence from the oven, and look for the center to be just set with a slight jiggle only when nudged. The aroma now becomes richer, with caramel and baked dairy notes. Baking within 15 to 20 minutes usually yields a silky center that slices cleanly after cooling. If you overbake the filling becomes dry and crumbly, so check early and err on the side of a slightly soft center which firms as it cools.
Sprinkle remaining toffee bits and butterscotch chips on top. Return to oven for 1 minute.: Once out of the oven, distributing the last toffee bits and butterscotch chips over the hot surface allows them to warm and just begin to melt where they touch, creating glossy spots and intensified flavor. Pop the pan back in the oven for about 1 minute , watching closely so the chips soften but do not fully collapse. The visual cue is a faint sheen on the chips and a slightly darker color on the toffee bits. A common mistake is leaving the bars in too long here, which can overmelt the chips and make the topping bleed into the filling.