Mash two of the bananas in a large mixing bowl with 2 tablespoons of the sugar until the mixture is mostly smooth.
Stir the mascarpone cheese into the mashed bananas until the mixture is well combined.
Whip the heavy cream and the remaining tablespoon of sugar in a separate bowl until stiff peaks form.
Gently fold the whipped cream into the banana and mascarpone mixture until uniform.
Pour the cooled coffee into a shallow dish and briefly dip the ladyfingers one by one, ensuring they are moistened but not soggy.
Arrange half of the dipped ladyfingers in the bottom of an 8-inch square baking dish, breaking them to fit if necessary.
Spread half of the banana cream mixture over the ladyfingers, then top with a layer of thinly sliced fresh banana and a dusting of 2 teaspoons of cocoa powder.
Repeat the layers with the remaining ladyfingers, banana cream, and sliced bananas.
Cover the dish and refrigerate for at least 3 hours to allow the ladyfingers to soften and the flavors to meld.
Dust the top with the remaining 2 teaspoons of cocoa powder just before serving.