Preheat the oven to 350°F (180°C). Grease a Bundt pan with nonstick spray.
In a medium bowl, whisk together the cream cheese, powdered sugar, and vanilla, stirring until smooth. Refrigerate.
In a large bowl, mash the bananas with a fork. Add the flour, sugar, baking powder, oil, egg, baking soda, salt, cinnamon, and vanilla. Stir until just combined, without overmixing. Pour half of the batter into the prepared Bundt pan.
With an ice cream scoop, scoop the cream cheese mixture evenly onto the cake batter in the pan, making sure that it does not touch the sides. Pour the rest of the banana bread batter on top and smooth it evenly.
Bake for 30 minutes, or until the banana bread is golden.
To make the caramel glaze, heat the sugar in a medium saucepan over medium-high heat. Once it begins to melt, stir with a wooden spoon or whisk. When it reaches a boil, add the butter and stir until melted. Remove from the heat, add the heavy cream, and immediately stir until incorporated. (Make sure the cream is at room temperature or else it will curdle the sauce.) Allow the caramel cool and thicken.
Invert the banana bread onto a wire rack set over a baking sheet.
Pour the caramel glaze over the cake, letting the excess drip off. Once the glaze has set, slice the cake.