Prepare the Pudding Base: In a medium saucepan, combine the coconut milk, sugar, and salt. Heat over medium heat, stirring occasionally, until the mixture is warm and the sugar has dissolved.
Thicken the Mixture: In a small bowl, mix the cornstarch with a few tablespoons of cold coconut milk until smooth. Gradually add this mixture to the saucepan, stirring constantly to avoid lumps. Continue to cook and stir until the mixture thickens and starts to bubble.
Add Flavor: Remove the saucepan from heat and stir in the vanilla extract.
Add Bananas: Slice the ripe bananas and gently fold them into the pudding mixture.
Chill: Pour the pudding into individual serving dishes or a large bowl. Cover with plastic wrap, pressing it directly on the surface of the pudding to prevent a skin from forming. Refrigerate for at least 2 hours or until chilled and set.
Serve: Enjoy the pudding as is, or top with additional sliced bananas, toasted coconut, or a dollop of whipped cream before serving.