Preheat the oven to 350 degrees F. Lightly grease a 13 by 9 by-2-inch baking pan.
For the cake: In the bowl of an electric mixer, combine the cake mix, egg, and butter and mix well. Pat into the bottom of prepared pan and set aside.
For the filling: Still using an electric mixer, beat the cream cheese until smooth. Beat in the eggs and vanilla. Dump in confectioners' sugar and beat well. Reduce the speed and slowly pour in butter. Mix well. Fold in toffee bits.
Pour filling onto cake mixture and spread evenly. Bake for 40 to 50 minutes. Don't be afraid to make a judgment call on the cooking time, because oven temperatures can vary. You want the center to be a little gooey, so don't bake it past that point!
Remove from oven and allow to cool completely. Cut into squares. Just remember that these wonderful cakes are very, very rich, and a little will go a long way.