Combine dry ingredients in a medium saucepan by whisking together the sugar, cornstarch, and salt until well blended. This even distribution prevents lumps from forming in your pudding.
Gradually whisk in milk until smooth, then add the beaten egg yolks, stirring constantly to incorporate them fully. The slow addition here is crucial for a silky-smooth texture.
Cook the mixture over medium heat, whisking constantly, until it thickens and begins to bubble, about 8-10 minutes. Once bubbling, continue cooking for 1-2 more minutes to fully activate the cornstarch.
Remove from heat and stir in butter and vanilla until the butter is completely melted and incorporated. The residual heat will melt the butter while the vanilla adds that signature aroma.
Transfer pudding to a bowl and press plastic wrap directly onto the surface to prevent a skin from forming. Allow to cool at room temperature for 30 minutes.
Slice bananas into ¼-inch thick rounds while the pudding cools. Don’t slice them too early or they’ll brown.
Assemble the dessert by placing a layer of vanilla wafers on the bottom of your serving dish, followed by a layer of banana slices, then top with one-third of the pudding. Repeat these layers twice more, ending with pudding.
Whip the heavy cream with powdered sugar and vanilla extract until stiff peaks form. This should take about 3-4 minutes with an electric mixer.
Top the pudding with the freshly whipped cream, spreading it evenly across the surface or creating decorative swirls.
Refrigerate for at least 3 hours or preferably overnight to allow the flavors to meld and the cookies to soften into cake-like layers.