Preheat the oven to 350°F.
In a medium bowl, combine graham cracker crumbs, ⅓ cup sugar, and melted butter. Mix until well combined.
Press the mixture firmly into the bottom and up the sides of a 9-inch pie pan. Bake for 8-10 minutes until golden brown. Remove from the oven and let cool completely.
In a medium saucepan, whisk together the milk, ¾ cup sugar, cornstarch, and salt. Cook over medium heat, stirring constantly until the mixture thickens and begins to bubble, about 5-7 minutes.
Remove from heat. Gradually whisk a small amount of the hot mixture into the beaten egg yolks, then return the egg mixture to the saucepan. Cook for an additional 2 minutes, stirring constantly.
Remove from heat and stir in 2 tablespoons of butter and 1 teaspoon of vanilla extract. Let cool slightly.
Layer half of the banana slices in the cooled pie crust. Pour half of the custard over the bananas, then add the remaining banana slices and top with the remaining custard.
Cover with plastic wrap and refrigerate for at least 4 hours or until set.
In a mixing bowl, beat the heavy whipping cream, powdered sugar, and 1 teaspoon of vanilla extract until soft peaks form.
Spread the whipped cream over the top of the pie before serving.