Whisk together granulated sugar, flour, and salt in a heavy bottom saucepan.
Add in the egg yolks to the saucepan and 2 cups of milk. Whisk together until smooth. Add in the remaining 3 cups of milk and whisk together again until well combined.
Cook over medium heat, stirring constantly until the pudding simmers and thickens (10-15 minutes).
Once the pudding thickens, remove from heat and add butter and 2 teaspoons vanilla.
In the bottom of a 13 x 9 casserole dish, layer half the vanilla cookies. On top of the cookies add half the pudding, then add in ALL of the bananas. Repeat with remaining cookies and pudding.
Preheat the oven to 325° and make your meringue.
Beat the egg whites with an electric mixer or hand-held mixer with a whisk attachment until foamy. Increase the mixer to high speed, gradually add powdered sugar and keep beating until stiff peaks form.
Briefly mix in 1 teaspoon vanilla extract.
Top the banana pudding with the finished meringue, fully covering the entire dish.
Bake for 12 to 15 minutes or until the meringue is golden brown.
Serve warm or chilled.
NOTE: Bananas need to be fully ripe, or they will create a chewy texture that is NOT pleasant during the baking process.
Old Fashioned Banana Pudding https://www.amodernhomestead.com/old-fashioned-banana-pudding/