Combine sugar, salt, and cornstarch in a bottom heavy, large sauce pot and mix. Pour in cold milk, heavy whipping cream, and vanilla extract and whisk well.
Heat it all over medium to medium-low heat while you slowly whisk until thickens and starts to bubble. Don't let is get to boil, bubble hard, of cook longer. Take off heat.
In a separate metal mixing bowl, whisk together eggs and egg yolks.
Very slowly, pour in 1/2 cup of milk mixture into the eggs while constantly whisking. This will warm up the eggs gradually to prevent scolding the eggs.
Pour in another 1/2 cup of milk mixture, very slowly, as you keep whisking.
Carefully, pour in the egg mixture from the bowl back into the sauce pot with milk mixture while slowly whisking.
Return the pot to the stove over medium-low heat. Cook for a few more minutes, stirring slowly and constantly, until mixture thickens more and starts to bubble. Remove from heat and let it cool to room temperature.
Assembling Banana Pudding:
Slice bananas into thin slices.
Line bottom of a serving dish or baking dish with half of the vanilla wafers and then half of the sliced bananas. (You can use a 9x13 baking dish, 9x9 baking dish with tall sides, glass round serving dish, or trifle bowl.)
Spread half of the cooled custard over the bananas and wafers.
Repeat the cookie, banana, and custard layers.
Do NOT add whipped cream to warm or hot pudding. Make sure that the pudding is no warmer than room temperature.
Place the metal mixer bowl and the whisk attachment into the freezer for 10-15 minutes. (If using glass mixer bowl, place it in the refrigerator for about 20 minutes.)Don't take the heavy whipping cream out of the refrigerator until actually ready to pour it into the bowl.
Add the cold heavy whipping cream into the cold mixing bowl and add powdered sugar, and vanilla extract. Starting at low speed, start whipping everything and gradually raise to speed to high every couple of seconds. Beat until stiff peaks appear (don't walk away far).
Transfer the whipped cream into a piping bag if you want to decorate the top or simply spread the whipped cream over the top of the pudding.
Cover the dish with plastic wrap and refrigerate for at least 4 hours.