Preheat oven to 350°F (175°C).
In a mixing bowl, combine graham cracker crumbs, sugar, and melted butter. Press mixture into a pie dish to form the crust.
Bake crust for 10 minutes. Let cool.
In a saucepan, combine milk, sugar, flour, and salt. Cook over medium heat, stirring constantly, until thickened.
Stir a small amount of hot mixture into beaten egg yolks, then return to saucepan. Cook for 2 more minutes, stirring constantly.
Remove from heat and stir in butter and vanilla extract.
Arrange banana slices on the cooled crust. Pour pudding mixture over bananas.
Chill in the refrigerator for at least 2 hours before serving.