Preheat the oven to 350 degrees. Lightly grease a 9 x 13-inch baking pan.
CAKE: In a large bowl, combine cake mix, egg, and melted butter, mix well with an electric mixer. Pat the mixture into the bottom of the prepared baking pan.
FILLING: In a large bowl, beat the cream cheese and pumpkin until smooth. Add eggs, vanilla, and butter; beat until combined. Slowly add the confectioners' sugar, cinnamon, and nutmeg, mix well. Spread the pumpkin mixture over the cake batter
Bake for 40 to 50 minutes. Make sure not to overbake as the center should be a little gooey. Remove from oven and allow to cool completely before cutting into squares. Serve with fresh whipped cream if desired.