Combine 2 cups of the cream, the milk, 1/2 cup of the sugar, the vanilla bean, and the vanilla seeds in a large heavy-bottomed saucepan over medium heat. Bring to a gentle boil, whisking to dissolve the sugar. Remove from the heat.
Combine the egg yolks, eggs, cornstarch, and 1 cup of the sugar in a medium bowl, and whisk pale yellow in color. Set aside.
Whisk 1 cup of the hot cream mixture into the egg yolks. Gradually add the egg mixture to the hot cream, whisking constantly. Bring to a simmer, stirring constantly with a large wooden spoon to cook out the cornstarch and the mixture thickens, about 5 minutes. (The mixture may separate slightly. If so, remove from the heat and beat with an electric mixer until thick and smooth.) Strain through a fine mesh strainer into a clean bowl. Cover with plastic wrap, pressing down against the surface to prevent a skin from forming. Chill in the refrigerator for about 4 hours.
To assemble, spread 1/2 cup of the custard over the bottom of the prepared crust, smoothing with the back of a large spoon or rubber spatula. Arrange enough banana slices (not quite one-third) in a tight, tiled pattern over the custard, pressing down with your hands to pack them firmly. Repeat to build a second layer, using 3/4 cup of the custard and enough bananas to cover, smoothing down the layer evenly. For the third layer, spread 3/4 cup of custard over the bananas and top with the remaining bananas, starting 1-inch from the outer edge and working toward the center. Spread 1 cup of custard evenly over the bananas to prevent discoloration. Cover with plastic wrap and chill for at least 4 hours or overnight.
In a medium bowl, whip the cream until soft peaks form. Add the remaining 2 teaspoons of sugar and the vanilla extract and whip until stiff peaks form.
Remove the pie from the refrigerator. With a sharp knife dipped in hot water, cut the pie into 10 equal slices. Transfer the slices to dessert plates. Fill a pastry bag with the whipped cream and pipe onto each slice. (Alternately, spread the whipped cream evenly over the pie before cutting.)
Drizzle each slice with the caramel sauce and chocolate sauce, sprinkle with the chocolate shavings and confectioners' sugar, and serve.
Combine the graham cracker crumbs and sugar in a medium bowl and mix well. Add the butter and mix well. Press the mixture into a 9-inch pie pan. Top with aluminum pie tin and with a circular motion, press the crust tightly into the pan. Bake until browned, about 25 minutes. Cool for 10 to 15 minutes.
Combine the sugar, water, and lemon juice in a medium, heavy saucepan over medium-high heat. Cook, stirring, until the sugar dissolves. Let boil without stirring until the mixture becomes a deep amber color, 2 to 3 minutes, watching closely so it doesn't burn. Add the cream, whisk to combine, and remove from the heat. Add the milk, 2 tablespoons at a time, until the desired consistency is reached. Remove from the heat and cool to room temperature before serving with the pie. (The sauce will thicken as it cools.)
Scald the half-and-half and butter in a small, heavy saucepan over medium heat. Remove from the heat.
Place the chocolate and vanilla in a medium, heat-proof bowl. Add the hot half-and-half and let sit for 2 minutes, then whisk until smooth. Serve slightly warm. (The sauce can be kept refrigerated in an airtight container for several days, but it must be returned to room temperature before serving.