Combine the cake mix, egg, and butter and mix well with an electric mixer. Pat the mixture into the bottom of a lightly greased 13 by 9- inch baking pan.
To make the filling: In a large bowl, beat the cream cheese and pumpkin until smooth. Add the eggs, vanilla, and butter, and beat together. Next, add the powdered sugar, cinnamon, nutmeg, and mix well. Spread pumpkin mixture over cake batter and bake for 40 to 50 minutes. Make sure not to overbake as the center should be a little gooey.