In a medium saucepan, whisk together sugar, flour, and salt over medium heat. Gradually add in milk while continuously stirring to prevent lumps. Cook until thickened and bubbling, about 10 minutes, then lower heat and cook for 2 more minutes.

Whisk eggs in a small bowl. Temper the eggs by slowly adding spoonfuls of hot custard, stirring well, then combine back into saucepan. Heat over low until gently boiling, for about 2 more minutes while stirring.

Remove from heat and stir in vanilla extract. Allow custard to cool for 15 minutes, stirring occasionally.

Layer about 25 vanilla wafers in an ungreased 8x8 dish, followed by half the sliced bananas, then pour half the cooled custard. Repeat with another layer of wafers, bananas, and custard.

Cover tightly with plastic wrap and refrigerate for at least 4 hours, preferably overnight.

Before serving, crush a few remaining wafers and sprinkle on top. Serve chilled.