In a medium saucepan, combine sugar, flour, and salt. Gradually whisk in the milk over medium heat. Cook, stirring constantly, until the mixture thickens and coats the back of a spoon (about 5–7 minutes). Remove from heat and stir in vanilla extract.
Layer the Pudding:
In a serving dish or individual cups, place a layer of vanilla wafer cookies at the bottom. Top with a layer of banana slices, then pour a layer of warm custard over the bananas. Repeat layers until all ingredients are used, finishing with a layer of custard on top.
Chill and Set:
Cover the pudding with plastic wrap and refrigerate for at least 2–3 hours, allowing it to set and the flavors to meld.
Serve:
