Mix graham cracker crumbs, 1/4 cup sugar, and 1/3 cup melted butter in a bowl; press mixture into a 9-inch pie dish to form a crust.
Bake in preheated oven until firm, 5 to 10 minutes.
Whisk milk, 1/2 cup sugar, cornstarch, flour, and salt in a saucepan over medium heat; bring to a boil, stirring constantly. Boil for 2 minutes, then add egg yolks while continuously stirring. Continue to cook and stir until thickened, about 1 minute more, and remove from heat. Stir in 1 tablespoon butter and vanilla extract. Allow vanilla mixture to cool for 10 minutes before pouring into prepared crust. Let pie come to room temperature.
Preheat oven to 425 degrees F (220 degrees C).
Beat egg whites in a glass or metal bowl until foamy. Gradually add 1/4 cup sugar, continuing to beat until stiff peaks form. Lift your beater or whisk straight up: the meringue will form sharp peaks. Spread meringue over vanilla pudding.
Bake in preheated oven until lightly browned, about 5 minutes. Let cool to room temperature.