Prepare the topping: Preheat the oven to 350'F. Grease a 9-inch round cake pan with nonstick spray and line with parchment. Place the bananas cut side down on the parchment, arranging or trimming to fit. In a medium saucepan, combine the sugar and water over medium-high heat. Cook, shaking the pan if needed, until an amber caramel forms, about 6 minutes. Immediately pour over the bananas in an even layer.
Prepare the batter: In a large bowl, whisk the brown sugar and mashed bananas until a relatively smooth paste forms. Whisk in the olive oil, yogurt, vanilla, and eggs until well incorporated.