Preheat oven to 350°F (175°C). Grease a 9×13-in baking pan.
Mix cake mix, egg, and melted butter in a bowl. Press into the pan to form the base.
In another bowl, beat cream cheese until smooth. Add eggs, vanilla, melted butter, powdered sugar, and cocoa powder. Mix well.
Pour the filling over the base layer without stirring. Let it settle naturally.
Bake for 40–50 minutes, until the top is golden and set, but the center remains slightly soft.
Cool for 10 minutes, then slice and serve warm or at room temperature.