Combine the milk and butter in a medium saucepan over medium-low heat, stirring gently to melt the butter.
Mix together 5 tablespoons of sugar and the cornstarch in a small bowl. Add 2 tablespoons water and mix to create a paste, and then whisk into the milk mixture. Raise the heat to medium and cook, stirring, until thick and bubbly, 7 to 10 minutes. Remove from the heat and stir in the vanilla extract.
Transfer to a bowl, cover with plastic wrap (make sure the plastic is touching the pudding to prevent a skin from forming) and refrigerate for at least 4 hours.
Combine the whipping cream with the remaining 1 tablespoon sugar in a bowl. Beat with an electric mixer until stiff peaks form. Set aside.
Create a layer of wafers on the bottom of an 8- by 8-inch dish, and then add a layer of bananas and a layer of pudding. Repeat to make a second layers. Top with whipped cream. Cover and refrigerate for 8 hours or overnight before serving.