In a medium saucepan, whisk together the sugar, cornstarch, and salt.

Gradually pour in the milk while whisking continuously to prevent lumps.

Heat over medium heat, stirring constantly until the mixture thickens and bubbles, about 5 minutes.

Remove from heat and stir in vanilla extract.

In an 8-inch square dish, layer half of the sliced bananas at the bottom.

Pour half of the pudding over the bananas, covering them completely.

Repeat the layers with remaining bananas and pudding.

Chill in the refrigerator for at least 2 hours before serving.