In a saucepan, whisk together 1 cup of sugar, flour, and salt. Gradually whisk in the milk until smooth. Cook over medium heat, stirring constantly, until the mixture thickens and comes to a boil.

Remove from heat and temper the egg yolks by slowly whisking a small amount of the hot pudding into them, then gradually add the tempered yolks back into the saucepan. Return to low heat and cook for 1-2 minutes, stirring constantly, until slightly thicker. Stir in 1 teaspoon of vanilla extract.

Arrange a layer of vanilla wafers in the bottom of a 9x13 inch baking dish. Top with a layer of sliced bananas, then pour half of the hot pudding over the bananas. Repeat the layers with more wafers, bananas, and the remaining pudding.

In a clean bowl, beat the egg whites with an electric mixer until soft peaks form. Gradually add 1/4 cup of sugar and 1/2 teaspoon of vanilla extract, continuing to beat until stiff, glossy peaks form.

Spread the meringue over the hot pudding, ensuring it touches the edges of the dish to prevent shrinking. Bake in a preheated oven at 350°F (175°C) for 15-20 minutes, or until the meringue is golden brown. Let cool slightly before serving or chill for several hours for best results.