Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together the softened butter and the yellow cake mix until well combined and crumbly. Stir in the 2 eggs, one at a time, until a dough forms. Press this dough evenly into the bottom of the prepared baking pan.
In a separate medium bowl, whisk together the melted butter, softened cream cheese, and 2 eggs until smooth. Stir in the vanilla extract.
Gradually beat in the powdered sugar until the mixture is smooth and pourable.
Pour the topping mixture evenly over the cake base in the pan.
Bake for 35-40 minutes, or until the edges are golden brown and the center is set but still slightly gooey.
Let cool completely in the pan before cutting and serving.
Notes
This cake is best served at room temperature. It can be stored in an airtight container at room temperature for up to 3 days.