Add milk and cream to a medium saucepan over medium heat. Bring to a simmer, stirring often.

In a medium bowl, whisk together the eggs, sugar, and cornstarch until well blended.

Spoon a little of the hot milk over the egg mixtures and whisk well. Repeat with another few spoonfuls of the hot milk, to temper the eggs.

Pour the egg mixture into the saucepan and continue to cook over medium low heat for 5-8 minutes until thickened.

Once thickened, remove from the heat and stir in the butter, vanilla extract, and salt.

Pour the pudding through a sieve or fine mesh strainer into a container, to remove any lumps and make it silky smooth.

Place a piece of plastic wrap directly on top and refrigerate for an hour or more, until chilled. Stir well once chilled.

To assemble the banana pudding, use a 9 inch square pan or individual dishes. Line the bottom with vanilla wafers, top with sliced bananas, then half of the pudding mixture. Repeat with another layer, and end with a final layer of wafers.

Cover tightly with plastic wrap and place the assembled dessert in the fridge for 4-8 hours.

Top with fresh whipped cream before serving, if desired.