Slightly adapted from Paula Deen.
First Layer
1 (15.25-ounce) package chocolate cake mix
1 egg
1 stick butter, melted
Second Layer
1 (8-ounce) package cream cheese, softened
2 eggs
3 to 4 tablespoons cocoa powder
1 (16-ounce) box powdered sugar
1 stick butter, melted
1 teaspoon vanilla extract
Preheat oven to 350ºF. Grease a 9-inch springform cake pan.
Combine the cake mix, 1 egg, and 1 stick melted butter, and stir until well blended. Pat the mixture into prepared pan and set aside.
In a stand mixer on medium speed, beat the cream cheese until smooth. Add the remaining 2 eggs, and the cocoa powder.
Lower the speed of the mixer and add the powdered sugar. Mix until everything is well combined. Slowly add the remaining 1 stick of melted butter and vanilla and continue to beat the mixture until smooth.
Pour filling over cake mixture in pan. Bake for 40 to 50 minutes. Be careful not to overcook the cake; the center should still be a little gooey when finished baking. Let cake partially cool on a wire rack before cutting into pieces.
http://pattietierney.blogspot.com/2015/11/not-so-ooey-gooey-chocolate-cake.html