In a small bowl, whisk egg yolks, then whisk in about 1/2 cup of hot custard until blended. Pour yolk mixture back into saucepan of custard; cook over medium heat, stirring, 2 minutes. Stir in butter and vanilla until blended.
Place vanilla wafers on bottom of a shallow 2-quart casserole dish. Top with layers of banana slices and custard. Repeat layering, ending with custard.
In a large mixing bowl, beat egg whites and 1/4 cup sugar at low speed until frothy. Add cream of tartar; increase speed to medium and gradually beat in remaining sugar. Beat until egg whites hold stiff peaks.
Spoon meringue over hot custard immediately, making sure that meringue touches baking dish on all sides (this prevents it from shrinking). Transfer to oven and bake until golden, about 20 minutes. Remove pudding from oven and cool 1 hour. Refrigerate at least 4 hours before serving.