In a medium saucepan, combine 3/4 cup sugar and 1/4 cup cornstarch, whisking together thoroughly. Gradually pour in 4 cups of whole milk while continuously stirring to avoid lumps. Cook over medium heat, stirring frequently until it thickens and bubbles, about 10 minutes. Remove from heat.

Add 2 tablespoons of butter and 1 tablespoon vanilla extract to the thickened pudding, stirring gently until fully melted and incorporated. Let cool for about 10 minutes.

In a separate bowl, whisk together 3 large eggs until smooth. Gradually add about a cup of the warm pudding to the eggs, whisking constantly to temper them. Return the mixture to the saucepan and cook over low heat for another 2-3 minutes until thickened, then remove from heat.

In a large serving dish, layer vanilla wafers, sliced bananas, and pudding. Repeat the layers until all ingredients are used, finishing with pudding on top.

Cover tightly with plastic wrap or a lid and refrigerate for at least 4 hours or overnight for best flavor.

Serve with a dollop of whipped cream and optional chocolate shavings or crushed vanilla wafers on top.