Place bananas, milk, and whipping cream into a heavy saucepan over medium heat. After the milk mixture has warmed, mash the bananas. Do not boil the mixture, just slowly bring it up to a hot temperature. (Too hot too fast can scorch the milk, so patience is key.)

In a separate small bowl, mix the sugar, cornstarch and salt together. When the milk mixture is nearly at a boil, add in the sugar mixture, stirring well to incorporate.

In a small dish, mix the egg yolks together. Add in some of the hot milk mixture a little at a time, about 1/2 cup total, to temper the eggs. Return this mixture to the heavy saucepan.

Bring to a gentle boil and boil for about 2 minutes. Remove from heat and stir in vanilla. If making individual servings, pour into 4 ramekins, otherwise pour into one larger serving bowl.

If you prefer to eat the pudding warm, serve immediately. Otherwise chill the pudding in the fridge, covering with plastic wrap.