Prepare the oven and baking dish. Preheat the oven to 350°F. Lightly grease a 9 x 13-inch baking dish and set aside.

Add the whole milk, ½ cup granulated sugar, egg yolks, and cornstarch to a medium saucepan. Whisk until completely combined and smooth.

Place the saucepan over medium heat. Cook for 7 to 10 minutes, whisking or stirring constantly, until the pudding thickens and begins to gently bubble.

Remove the saucepan from the heat. Add the butter and 1 teaspoon vanilla extract. Stir until the butter has completely melted and the pudding is smooth.

Spread a thin layer of warm pudding over the bottom of the prepared baking dish.

Arrange a layer of vanilla wafers over the pudding. Top the wafers with an even layer of sliced bananas.

Pour half of the remaining warm pudding over the bananas. Add another layer of vanilla wafers followed by another layer of sliced bananas.

Pour the remaining pudding evenly over the top, making sure the bananas are covered.

Add the room-temperature egg whites and cream of tartar to a clean mixing bowl. Using an electric mixer, beat until soft peaks form.

Gradually add 3 tablespoons granulated sugar while continuing to beat the egg whites. Beat until the meringue forms stiff, glossy peaks.

Add ½ teaspoon vanilla extract and mix just until incorporated.