How to Make It
In a 9-inch square baking dish, arrange half of the wafers in a single layer. Top with half of the bananas. Repeat with the remaining wafers and bananas.
In a medium bowl, whisk the sugar with the flour. In a large saucepan, gently heat the milk until hot but not bubbling. Whisk in the sugar mixture in three batches, then whisk in the egg yolks. Cook over moderate heat, stirring frequently, until the custard is thickened and pudding-like, 5 to 8 minutes. Whisk in the butter and vanilla. Pour the hot custard over the wafers and let stand at room temperature for 20 minutes. Refrigerate until chilled, then cover and refrigerate overnight.
In the bowl of a stand mixer fitted with the whisk, combine the egg whites, vanilla and cream of tartar. Beat at high speed until soft peaks form, 1 to 2 minutes. With the machine on, add the sugar 1 tablespoon at a time; beat until smooth, glossy, just-firm peaks form, about 2 minutes. (Do not overbeat or the meringue will become grainy.) Spread the meringue evenly over the banana pudding, swirling it decoratively. If you have a kitchen torch, you can brûlée the meringue if desired.