Preheat the oven to 350F, and butter a 9" springform pan thoroughly. Place the pan on a baking sheet lined with foil to catch any spills.
In a small bowl, combine the melted butter and brown sugar for the topping, and spread it in the bottom of the cake pan. Top with the halved bananas.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In the bowl of a stand mixer, beat together the butter and sugar for the cake until light and fluffy. Add in the eggs, one at a time, followed by the vanilla and mashed bananas.
Add in half of the flour mixture, followed by the Greek yogurt, followed by the rest of the flour. Finally, stir in the chocolate chips, and pour the cake batter into the pan.
Bake for 55-60 min, until the cake no longer juggles and a toothpick inserted in the center comes out mostly clean.
Let cool slightly before flipping and removing from pan.