Mix the milk, mashed banana and vanilla in a medium saucepan.
Cook over medium heat for about 5 minutes, stirring occasionally, until the mixture is steaming.
Meanwhile, beat together the egg yolks, granulated sugar, cornstarch, and salt in a large bowl until light and fluffy, 2 to 3 minutes.
Pour 1⁄4 of the heated milk into the egg yolk and stir until well blended.
Then slowly add the remaining milk, beating with a whisk.
Pour the mixture back into the saucepan, cook over medium heat, stirring with a whisk, until the mixture thickens and begins to simmer, 4 to 6 minutes.
Remove from the heat and add the butter, stirring constantly with a whisk.
After having passed it in a fine mesh sieve; discard any lumps and pour the ready cream into a clean bowl.
Arrange the banana slices in a single layer on the bottom of the cooled base. Spread the custard evenly over the sliced bananas.
Cover, adhering the plastic wrap directly to the surface of the custard, and refrigerate until the custard has set, from 4 hours to a day.