Preheat oven to 400 degrees F (200 degrees C.)

Combine sugar, cornstarch, and salt for custard in a large saucepan or double boiler until well mixed. 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 vanilla.

Pour 1/2 of the custard into baked pie shell. Cover with sliced banana. Spread remaining custard over banana layer.

Beat egg whites and cream of tartar for meringue topping in a large glass or metal mixing bowl until foamy. Gradually add 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.