Preheat oven to 350 degrees. Lightly grease a 13x9x2-inch baking pan. In the bowl of an electric mixer, combine cake mix, egg, and butter and mix well. Pat into the bottom of prepared pan and set aside.
Still using an electric mixer, beat cream cheese until smooth; add eggs and vanilla. Dump in confectioners' sugar and beat well. Reduce speed of mixer and slowly pour in butter. Mix well.
Pour filling onto cake mixture and spread evenly. Sprinkle chocolate chips and nuts on top of filling. 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.
*Variations: Pumpkin Gooey: For the cake part, use a spice cake mix or a basic yellow cake mix. Follow the original recipe, adding a 15-ounce can of pumpkin pie filling and an extra egg to the cream cheese filling. Bake as usual, remove from oven, and allow to cool. Cut into squares and top each square with a pecan half. Serve with a dollop of fresh whipped cream.
Peanut Butter Gooey: Use a chocolate cake mix. Add 1 cup creamy peanut butter and an extra egg to cream cheese filling. You can sprinkle the top of batter with 1 cup chopped peanuts if you like. Proceed as directed above.