Make the pudding. Place half-and-half, whole milk, 1/2 cup sugar, and salt in a medium saucepan with a heavy bottom. Bring to a simmer over medium heat, stirring occasionally to help dissolve the sugar.
Place 4 egg yolks in a medium bowl and add remaining 1/4 cup sugar. Whisk together well. Whisk in 3 tablespoons cornstarch until combined well, about 30 seconds.
When half-and-half mixture comes to a simmer, use a measuring cup to scoop out about 1 cup of the mixture. (Go ahead and turn the heat down some so it will not go beyond a slow simmer. Very gradually add it to egg mixture while whisking constantly to temper the eggs.
Pour egg mixture into saucepan. Stir over medium heat for 2 to 3 minutes, until mixture is thickened. Remove from heat and stir in butter pieces and vanilla. If any of the egg curdles, pour the pudding through a fine-mesh strainer, pressing through with the back of a spoon.
To assemble, cover the bottom of a 2-quart casserole dish with a thin layer of pudding mixture.
Top with a layer of Nilla Wafers and then a layer of banana slices. Repeat layers, until all pudding is used.
Spread whipped cream on top. Refrigerate for at least 4 hours before serving.
