Whisk together sugar, flour, and salt in a medium saucepan with a heavy bottom.
Add the egg yolks and 1 cup of milk. Whisk until smooth and then whisk in the remaining 2 cups of milk.
Place over medium heat and cook until it simmers and is thickened. This will take about 10 to 15 minutes. You want to stir it almost constantly during this time. It's ok to take a few quick 5 to 10 second breaks, but you don't want to go much longer than that.
Once thickened, remove from heat and stir in vanilla and butter.
Place a layer of Vanilla wafers in the bottom of a 2-quart baking dish. You want to use half of the vanilla wafers.
Arrange half of the banana slices over the Vanilla wafers.
Pour half of the pudding mixture over the bananas.
Preheat oven to 325 degrees.
To make the meringue, beat the egg whites and cream of tartar with an electric mixer until foamy. Gradually add sugar and keep beating on high speed until stiff peak form. Mix in the vanilla extract.
Spread the meringue on top of banana pudding, being sure to completely cover the pudding layer. Place on a baking sheet and bake for 12 to 15 minutes or until the meringue is golden brown.Serve warm or chilled.