Line the bottom and sides of a 9-inch-square baking dish with the vanilla wafers. Set aside.
Combine the brown sugar and flour in a medium saucepan set over medium heat; stir to combine. Add the milk, whisk, and bring to a boil over medium-high heat. Lower the heat to medium-low and simmer, whisking constantly, until thick, 3 to 4 minutes. Remove from the heat.
Whisk the eggs in a medium bowl. Gradually whisk about 3/4 cup of the hot milk mixture into the eggs. Return the egg mixture to the saucepan with the remaining hot milk mixture and bring to a boil. Lower the heat and simmer, whisking constantly, until smooth and thick, about 2 minutes. Remove from the heat and add the butter and vanilla. Whisk until the butter is melted and the mixture is smooth. Transfer to a clean bowl and cool to room temperature.
In a medium bowl, whip the cream until soft peaks begin to form. Add the confectioners' sugar and whip until stiff peaks start to form. Add the rum and whip to incorporate. Set aside in the refrigerator.
Pour half of the pudding over the vanilla wafers, then top with the banana slices. Add the remaining pudding, smoothing it over the bananas. Cover tightly and chill at least 2 hours before serving.
When ready to serve, top with the whipped cream, and smooth with the back of a spoon. Drizzle chocolate sauce over the cream and top with the walnuts.
Makes 8 to 10 servings