Preheat oven to 350°F (175°C).
In a saucepan, whisk together sugar, flour, salt, milk, and egg yolks. Cook over medium heat, stirring constantly until thick and smooth. Remove from heat and stir in vanilla extract.
In a baking dish, layer vanilla wafers, sliced bananas, and warm custard. Repeat layers, finishing with custard on top.
In a bowl, beat egg whites with sugar until stiff peaks form. Spread meringue over the pudding, sealing to the edges.
Bake for 12 minutes or until meringue is golden. Let cool slightly before serving, or chill before serving if desired.