Preheat the oven to 350°F. Grease an 8x8-inch square baking pan or 9-inch round cake pan. Lightly dust with sugar if desired.
In a medium bowl, mash the overripe bananas until mostly smooth. A few small lumps are fine.
In a large mixing bowl, whisk together the melted butter, dark brown sugar, granulated sugar, and maple syrup until well combined. Add the eggs and whisk until smooth.
Add in the sour cream, milk, and vanilla extract. Whisk until fully combined.
Fold in the mashed bananas.
Then add the flour, baking powder, baking soda, salt, cinnamon, and cornstarch to the wet ingredients. Gently fold or stir until just combined. Do not overmix.
Pour the batter into the prepared pan and spread it into an even layer. Bake for 35–40 minutes, or until the center is set and a toothpick inserted into the center comes out with a few moist crumbs.
Allow the cake to cool completely in the pan before frosting.
In a medium bowl, beat the softened butter and cream cheese until smooth and creamy.
Add the powdered sugar, vanilla extract, maple syrup, and a pinch of salt. Beat until smooth.
Add the half-and-half, or heavy cream, a little at a time until the icing reaches your desired smooth, spreadable consistency. You may not need the entire tablespoon.
Once the cake has cooled completely, spread the maple cream cheese icing evenly over the top.
Slice into squares or wedges and serve.