Preheat your oven to 350°F. In a food processor, blend graham crackers, melted butter, and sugar until it resembles damp sand. Press this mixture firmly into a pie plate and bake for 6-8 minutes until golden brown. Let it cool completely.

In a saucepan, whisk together egg yolks, sugar, cornstarch, salt, and milk. Cook over low-medium heat, stirring constantly until thickened to a custard-like consistency. Once thick, stir in butter and vanilla, then set aside to cool.

Slice the bananas and layer them evenly across the cooled crust. Pour half of the custard over the bananas, followed by another layer of bananas and the remaining custard. Smooth the top.

Spread whipped topping over the pie and refrigerate for at least 4 hours or until fully set.