Preheat oven to 350 degrees F. Grease and flour a 13"x9" pan. In a bowl, combine cake mix, butter, and two eggs. Batter will be very stiff. Spread in prepared pan. In another bowl, combine remaining two eggs, cream cheese, and powdered sugar. Beat until very smooth and pourable. Pour over crust. Bake in preheated oven for about 30 minutes, or until cake is nearly set. Top will be a light golden brown, and center should jiggle slightly. Let cake cool completely before cutting and serving.
Notes
I store the cake in the refrigerator, but I think you'd be fine with it at room temperature. I've also heard it freezes quite well.