Slice the bananas into 1/2-inch rounds and set aside in a bowl. Arrange the vanilla wafers and banana slices in alternating layers in a 9x13-inch baking dish, starting with a layer of wafers on the bottom. This creates a sturdy foundation that will absorb the custard beautifully. You'll typically get about 2-3 layers depending on your layering technique.

In a medium saucepan, whisk together the sugar, salt, and flour until well combined with no lumps. Add the egg yolks one at a time, whisking thoroughly after each addition to prevent scrambling. Gradually whisk in the milk and evaporated milk, stirring until smooth. This slow incorporation prevents lumps and ensures a silky custard texture. I prefer King Arthur all-purpose flour because it creates a smoother, more refined set than other brands.

Place the saucepan over medium heat and stir constantly for 7-8 minutes until the mixture thickens and coats the back of a spoon. You'll notice it transforms from thin and pourable to creamy and luscious. Remove from heat and stir in the vanilla and nutmeg. The evaporated milk is key here—it creates that extra-creamy richness that defines a proper banana pudding.

Pour the warm custard sauce from Step 3 evenly over the wafer and banana layers from Step 1, allowing it to soak into and around the wafers. Let it sit for a few minutes to fully absorb before moving to the meringue topping.

In a clean, dry bowl, beat the egg whites with an electric mixer on high speed until stiff peaks form (they should stand straight up when you lift the beaters). In a separate small bowl, combine the 1/2 cup sugar and 1.25 tsp vanilla. Gently fold this mixture into the beaten egg whites using a spatula, being careful not to deflate them—you want to maintain as much volume and stability as possible.

Spread the meringue topping evenly over the pudding, making sure it reaches all the edges and seals the entire surface (this prevents shrinking during baking). Bake in a preheated 350°F oven for 10-12 minutes until the meringue is lightly browned with golden peaks. Watch carefully—meringue can brown quickly. I always let the pudding cool for at least 15-20 minutes before serving so the layers set properly and it's easier to portion.