Pour 2 cups whole milk and 1 cup heavy cream into a medium saucepan over medium heat and bring to a gentle simmer.

In a mixing bowl, whisk together 5 large egg yolks, 1/2 cup granulated sugar, and 3 tablespoons cornstarch until the mixture turns pale yellow and ribbon-like.

Slowly pour 1 cup of the hot milk mixture into the egg mixture while whisking constantly to temper the eggs and prevent scrambling.

Pour the tempered egg mixture back into the saucepan with the remaining milk mixture, reduce heat to medium-low, and cook for 5 to 7 minutes, stirring frequently, until the pudding thickens and coats the back of a spoon.

Remove the saucepan from heat and stir in 2 teaspoons vanilla extract, 2 tablespoons butter, and 1/4 teaspoon salt until fully combined.

Slice 4 medium bananas on the bias into 1/4-inch thick pieces; melt 4 tablespoons butter in a small skillet over medium-high heat, add 1/4 cup brown sugar, and cook for 1 minute until bubbling.

Add the banana slices to the skillet and cook for 2 to 3 minutes per side without stirring to allow them to develop a caramelized crust.

Place 35 to 40 vanilla wafer cookies in a sealed bag and crush them with a rolling pin until you have coarse, varied crumbles.

Spread a thin layer of vanilla pudding in a 9x13 inch baking dish, top with caramelized bananas and a layer of wafer crumbles; repeat layers ending with wafer crumbles on top.

Cover the baking dish with plastic wrap and refrigerate for at least 2 hours to allow the pudding to set and flavors to meld.

Just before serving, pour 1 cup heavy cream into a clean bowl and whip with an electric mixer until soft peaks form, then add 2 tablespoons powdered sugar and whip for 30 seconds more.

Top each portion of pudding with a dollop of whipped cream and serve immediately.