Add eggs to a small mixing bowl and whisk until combined; set aside.
Add sugar, cornstarch, and salt to a medium saucepan and whisk until combined.
Slowly add in milk and whisk to combine.
Heat over a medium heat, stirring constantly to prevent burning.
Once the milk mixture is hot and steamy, but not boiling, slowly add about 1/4 cup of the hot milk mixture to the bowl of eggs to temper the eggs, being careful not to cause them to overcook and become scrambled.
Slowly pour the egg mixture into the pan with the hot milk mixture, stirring constantly.
Continue to heat over medium heat until the mixture starts to thicken. Once it starts to thicken, boil for 1 more minute then remove the saucepan from heat and add in the vanilla extract. Stir to combined.
Layer the bottom of an ungreased 8x8-inch square baking dish with 25-30 gluten free vanilla wafers (whatever fits). Top the wafers with half of the banana slices then half of the pudding.