Preheat your oven to 350°F. Line an 8x8-inch baking pan with parchment paper, leaving an overhang for easy removal, and lightly grease with cooking spray.
In a medium saucepan, melt the butter over medium heat. Stir in 3/4 cup brown sugar and cook, whisking constantly until. Let it bubble for about 30 seconds, then pour into the prepared pan.
Arrange the banana slices in a single layer over the caramel sauce, leaving a small space between each slice for even caramelization.
In a large mixing bowl, whisk together the egg, granulated sugar, oil, Greek yogurt, and vanilla extract. Mix in the mashed bananas.
Sift in the flour, baking powder, baking soda, and salt. Fold the dry ingredients into the wet mixture until just combined. Do not to overmix.
Gently pour the batter over the banana slices in the pan, smoothing the top with a spatula.
Bake for approximately 45 minutes, or until a toothpick inserted into the center comes out clean or with a few crumbs.
Allow the cake to cool in the pan for at least 3 hours to ensure the caramel sets properly.
To serve, lift the cake out of the pan using the parchment overhang, place a serving plate on top of the cake, and invert it so the caramelized bananas are on top.