In a large bowl, mix together the cake mix, egg, melted butter, and nutmeg (if using).
In a 7x9 baking pan lined with parchment paper, press the batter in an even layer.
In a large bowl, stir together the softened cream cheese, eggs, and vanilla extract.
Stir in the powdered sugar.
Pour this frosting batter over the top of the cake batter layer.
Bake at 350°F for 45 minutes. The edges will puff slightly and turn golden brown, while the center will remain very jiggly.
Remove from the oven and allow the cake to cool.
Refrigerate for at least two hours (covered) or overnight before cutting into bars.
The 7x9 baking pan I used is Staub brand, and although not necessarily a standard size (9x13 being more common), it is a common pan. However, you could use a 9x13 pan instead and reduce the baking time to 35-38 minutes.