In a large mixing bowl, use a fork to mash the ripe bananas.
3. Step
Whisk in the egg, followed by vegetable oil and milk. Mix until combined.
4. Step
Add in the yellow cake mix, being careful to not overmix.
5. Step
Use a rubber spatula to gently fold in the chocolate chips. Set aside.
6. Step
In a shallow saucepan, set over medium heat, add the butter and brown sugar, and stir constantly with a wooden spoon until the mixture turns into golden brown syrup, about 5 minutes.
7. Step
Pour the syrup into a 9-inch (20-cm) round cake pan. Place the sliced bananas into a single layer on top of the syrup.
8. Step
Divide the cake batter among the banana pan, and another greased 9-inch (20-cm) cake pan.
9. Step
Bake for 20-25 minutes, or until a toothpick comes out clean from the center.
10. Step
Once the banana bottom cake is cool to touch, invert onto a cooling rack set on top of a parchment paper-lined baking sheet. Leave the second cake to cool to room temperature inside the pan.
11. Step
In a large mixing bowl, whisk together the cream cheese and sugar until light and fluffy.
12. Step
Beat in the eggs, one at a time. Add in the sour cream and vanilla extract, and mix until combined.
13. Step
Pour the cheesecake batter into the cooled cake in the pan. Cover the bottom of the pan with two sheets of foil and place into a larger baking dish.
14. Step
Fill the baking dish with water until it comes 1 inch (2 cm) up the side on the cake pan.
15. Step
Bake for 1 hour. Turn the heat off and open the oven door and let cool for one hour. Refrigerate the cake for 4 hours.
16. Step
To assemble, remove the cheesecake from the springform pan. Top the cake with the cooled banana fosters cake.