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, cornstarch, and salt. Cook over medium heat, stirring constantly, until thickened.
Gradually whisk in beaten egg yolks. Cook for 2 more minutes, then remove from heat.
Stir in butter and vanilla extract. Let cool slightly.
Arrange banana slices in the cooled crust. Pour filling over bananas.
Chill pie in the refrigerator for at least 2 hours.
Top with whipped cream before serving.