In a large saucepan or double boiler combine sugar, cornstarch and salt. Mix well, then stir in milk and egg yolks. Whisk until all ingredients are thoroughly combined. Cook over medium heat, stirring constantly, until mixture is thickened. Remove from heat and stir in butter and 1 tablespoon vanilla.
Preheat oven to 400 degrees F (200 degrees C.) Pour half of custard into baked pie shell. Cover with sliced banana. Spread remaining custard over banana layer.
In a large glass or metal mixing bowl, beat egg whites and cream of tartar until foamy. Gradually add white sugar, continuing to beat until stiff peaks form. Beat in vanilla extract. Spread meringue over pie, covering completely.
Bake in the preheated oven for 10 to 15 minutes, or until lightly browned.