Preheat the oven to 350 degrees, and spray a 9- by 13- by 2-inch pan with cooking spray. Mix the cake mix, 1 egg and the softened butter together. Press it into the prepared pan. In the same bowl, mix the remaining eggs, cream cheese and vanilla, then beat in the powdered sugar. Pour over the top of the cake in the pan. Bake at 350 for 10 minutes, then lower the heat to 325 and bake another 40 to 50 minutes.