Start by making the graham cracker crust; in a medium size mixing bowl add your graham cracker crumbs, the brown sugar and the melted butter and mix well with a rubber spatula until well combined.
Add the mixture into a 9-inch pie dish and press down to form the crust. Bake the crust in the oven at 350ºF for 10 minutes or until the crust is golden brown. Allow to cool completely.
Meanwhile, make the filling; in a medium saucepan over medium heat combine the half and half, sugar, and salt. Whisk until the sugar has dissolved, then bring to a simmer whisking occasionally. In a medium heatproof bowl mix the egg yolks and cornstarch together until thick and smooth.
Slowly whisk 1 cup of the simmering milk into the egg yolk mixture. Then slowly whisk the egg yolk mixture into the pan. Cook the mixture, wicking continuously until it is thick and bubbles begin bursting at the surface, about 1-2 minutes.
Remove the pan from the heat and mix in the vanilla extract and butter. To prevent a “skin” from forming, place a plastic wrap on top of the warm pudding. Allow to cool for 15-20 minutes.
Slice 1 big banana (or 2 small ones) and arrange the slices into the cooled pie crust. Spread the cooled pudding on top. Place another piece of plastic wrap on top of the filling, to prevent the “skin” from forming. Refrigerate for at least 4 hours.
When you are ready to serve the banana cream pie, make the whipped cream; using a hand mixer or a stand mixer fitted with the whisk attachment, beat the heavy cream, confectioner’s sugar, and vanilla extract on medium-high speed until stiff peaks form, about 5 minutes.
Spread the whipped cream onto the chilled pie. Slice the remaining bananas and decorate the pie with the banana slices. Slice and serve.