Make the Pudding: Place the egg yolks in a small bowl and whisk lightly to combine.
In a medium saucepan, whisk together the sugar, cornstarch, and salt. Stir in the milk and cook over medium-low heat until slightly thickened. Gradually whisk a small amount of the hot milk mixture into the egg yolks.
Return the mixture to the saucepan, scraping the bowl with a rubber spatula; return to a simmer over medium heat, whisking constantly, until a few bubbles burst on the surface and the mixture is thickened and glossy, about 30 seconds. Off the heat, whisk in the butter and vanilla.
Strain the pudding through a fine-mesh sieve set over a medium bowl. Place plastic wrap directly on the surface of the pudding to keep a skin from forming.
Line the bottom of a 1½-quart serving dish or pie plate with vanilla wafers. On top of the wafers, place a layer of the sliced bananas. Pour ½ of the pudding over the bananas, and spread to the edges of the dish. Repeat the vanilla wafers, bananas, and pudding again. Press plastic wrap against the surface of the pudding and refrigerate for at least 4 hours or overnight.
Make the Whipped Cream: When ready to serve, whip the heavy cream with the powdered sugar and vanilla until stiff peaks form. Spread on top of the pudding and top with crushed vanilla wafers. Store leftovers in the refrigerator.
Notes
Serving, Storage, and Shelf-Life
Serving: Some simple ways to serve homemade banana pudding are in a 9x13 baking dish or in a pie pan (as shown in the pictures). You could also serve it up in a trifle bowl or make individual banana pudding's and serve them in ramekins!
Storage: Cover with plastic wrap or aluminum foil and store in the refrigerator.
Shelf-life: Covered properly, the banana pudding should last for about 3 days in the refrigerator.