Add your milk, salt, banana, and sugar to a pot and bring to a simmer on medium low heat for about 15-20 minutes.
In a bowl, whisk your egg yolks and cornstarch until well combined.
Remove the banana slices once the milk is hot.
Temper the eggs by slowing adding a large spoonful or 1/4 cup of the hot milk to the egg mixture and whisk constantly to avoid cooking the eggs. Once the egg mixture has reached the same temperature as the milk, add it to the remaining pot of milk.
Simmer for about 5 minutes or longer for really thick custard, whisky frequently. Reduce the heat as needed.
Remove from heat and add your butter and vanilla.
Strain your mixture for a smoother texture.
Cover the surface with plastic wrap to avoid a skin from forming on the surface.
Let cool before transferring to the refrigerate to set for at least 3 hours.