In a medium saucepan, combine 2 cups of milk, ½ cup granulated sugar, ⅓ cup cornstarch, and ¼ teaspoon salt. Heat over medium, stirring continuously for about 8-10 minutes until thickened.

In a separate bowl, whisk together 3 large eggs. Gradually add about a cup of the hot milk mixture to the eggs while whisking constantly to prevent curdling.

Pour the egg mixture back into the saucepan with the remaining pudding base, stirring to combine smoothly. Continue cooking for 2-3 minutes until thickened.

Remove from heat and stir in 2 tablespoons of unsalted butter and 1 tablespoon of vanilla extract until melted and combined.

Prepare a serving dish for layering. Place a layer of vanilla wafers at the bottom, followed by sliced bananas and a scoop of the creamy pudding.

Continue layering with vanilla wafers, sliced bananas, and pudding until all ingredients are used, finishing with pudding on top.

Cover with plastic wrap or a lid and chill for at least 2 hours to allow flavors to meld and pudding to set.