Preheat oven to 350°F. Grease a 9×13 pan with butter.

In a small saucepan over medium heat, melt the butter and brown sugar together until the mixture becomes slightly glossy, about 2 minutes (no more!). Pour mixture evenly into the pan. Place the sliced bananas on top of the brown sugar mixture. Set aside.

In a large bowl, mix together the mashed banana, melted butter, eggs, greek yogurt, sugar, and vanilla extract until combined. Stir in the baking powder and salt, then stir in the flour, mixing until just combined.

Spread the batter evenly on top of the bananas, and bake in the oven for 30 minutes, or until the top has started to turn golden brown along the edges and the brown sugar and butter bubbles up along the rim of the pan. Mmmmm.

Allow to cool for 10 minutes before inverting over a large tray. Cake is best served warm, possibly with a scoop of vanilla ice cream!