Slice the bananas into circles, cutting them about ¼” thick.
Place a layer of Nilla wafers in the bottom of an 8x8 pan, making a single layer of cookies across the bottom. Top the cookies with a single layer of banana slices, using about 2 bananas. It is okay if the banana slices overlap. Set the pan, extra banana slices and Nilla wafers aside.
In a medium sized sauce pan, whisk the sugar, flour and salt together. Whisk in the milk.
In a separate medium sized bowl, whisk the eggs, breaking them up slightly.
Put the saucepan with the milk on the stove and heat over medium heat, whisking occasionally to prevent the milk from burning on the bottom of the pan.
Once the milk starts to boil, whisk constantly for 2 minutes. The pudding will start to look thick. Remove the pot from the stove and whisk in the vanilla.
Scoop about ¼ cup of the hot pudding into the bowl with the eggs and whisk immediately so the eggs do not scramble. Pour this mixture back into the pot with the rest of the pudding and whisk again to incorporate the eggs into the mix.
Return the pot to the stovetop and cook for 2 more minutes, whisking the whole time. The pudding will look smooth and thick.
Pour half of the hot pudding into the 8x8 pan, covering the wafers and banana slices completely. Try to make a nice, even layer of pudding.
Add another layer of Nilla wafers to the pan followed by another layer of bananas. Try to use the rest of the banana slices in this layer.
Pour the rest of the pudding into the pan and smooth the top with a spatula or spoon.
Cover the pan loosely and place it in the fridge to set for about 4 hours.
Before serving, sprinkle some chopped wafers over the top of the pudding then scoop and serve!