Heat the oven to 350°F and whisk the milk, 3/4 cup sugar, flour, salt and egg yolks in a heavy saucepan.
Cook over medium heat for 8 to 10 minutes, whisking constantly, until the custard bubbles and coats a spoon, then stir in the butter and vanilla.
Layer half the wafers, half the bananas and half the hot custard in a 2 1/2-quart baking dish and repeat the layers.
Beat the egg whites and cream of tartar to soft peaks, gradually add the remaining 1/3 cup sugar, and beat to glossy stiff peaks.
Spread the meringue over the hot custard all the way to the dish edges.
Bake for 10 to 12 minutes until the peaks are toasted and the meringue reaches 160°F.
Cool for 30 minutes and refrigerate for 3 hours before serving.