To make the banana pudding, whisk the egg yolks, sugar, cornstarch, and salt together in a medium bowl and set aside. Bring the milk to a boil in a medium saucepan. Remove from the heat and whisk a little at a time into the egg mixture. Once the bottom of the bowl is warm, slowly whisk in the remaining hot milk. Pour the mixture back into a clean medium saucepan (cleaning the saucepan prevents the pudding from scorching), add the banana liqueur, and whisk over medium-low heat until it thickens, about 2 minutes. Cook while constantly whisking until the pudding is glossy and quite thick, 1½ to 2 minutes longer. Transfer the pudding to a clean bowl. Add the vanilla extract and butter to the bowl and gently whisk until the butter is completely melted and incorporated into the pudding. Press a piece of plastic wrap onto the surface of the pudding to prevent a skin from forming. Refrigerate for 4 hours.
For the chocolate sauce, bring water and corn syrup to a simmer in heavy medium saucepan. Reduce heat to low. Add both chocolates and stir until smooth. Remove from heat, set aside and keep warm.
To assemble, place banana pudding in serving bowls, add the sliced bananas, top with fresh whipped cream and drizzle with warm chocolate sauce.