Preheat your oven to 350°F. Place a very clean and dry stand mixer bowl in the refrigerator to chill for making the meringue.

In a medium saucepan, whisk together the flour, sugar, and salt. In a medium mixing bowl, whisk together the evaporated milk, whole milk, and egg yolks until combined.

Pour the milk mixture into the pan with the flour mixture and stir everything together with a silicone whisk. Heat the pudding over medium heat, whisking constantly until it reaches a thick but pourable consistency. This should take about 10 to 12 minutes.

Once the pudding has thickened, remove the pan from the heat and stir in the butter and vanilla bean paste until the butter is melted. Strain the pudding through a mesh strainer into a bowl and set it aside.

Remove the mixing bowl from the refrigerator and add the egg whites and salt. Beat the egg whites on low (a setting of 2 to 3) with a stand mixer fitted with the paddle attachment until frothy.

Add the cream of tartar to the egg whites and continue to beat on medium speed until larger bubbles form. Gradually add the sugar, 1 tablespoon at a time, and beat on medium-high speed until the meringue is glossy and stiff peaks form. Lastly, beat in the vanilla extract until it is no longer visible.

Arrange half the Nilla wafers in a layer on the bottom of a 9 x 13 baking dish. Slice the bananas and arrange half of them on top of the Nilla wafers. Immediately spread half of the vanilla pudding over the bananas in an even layer.

Repeat this process once more with the remaining Nilla wafers, bananas, and vanilla pudding. Spoon the meringue on top of the last layer of pudding and smooth it out into an even layer, making sure it reaches the edges of the dish. Create swoops and peaks with the back of a large spoon if desired.

If you have any leftover Nilla wafers, you can arrange them around the edge of the dish in a standing position. Bake the banana pudding in the preheated oven for 10 to 12 minutes until the meringue is browned. Serve banana pudding warm or chilled.