Prepare Baked Deep-Dish Pastry Shell. Reduce oven temperature to 300 degrees F. Meanwhile, place egg whites in a large bowl. Let stand at room temperature for 30 minutes.
For filling: In a medium saucepan, stir together granulated sugar and cornstarch. Stir in milk and chocolate. Cook and stir over medium heat until thickened and bubbly. Cook and stir for 2 minutes more. Gradually stir about 1 cup of the hot mixture into egg yolks. Return egg yolk mixture to saucepan. Bring just to boiling; reduce heat. Cook and stir for 2 minutes. Remove from heat. Stir in butter and vanilla. Cover and keep hot.
For meringue: Beat egg whites with an electric mixer on low speed until foamy. Add 1 tablespoon of the powdered sugar and the cream of tartar; beat until combined. Gradually add the remaining powdered sugar, 1 tablespoon at a time, beating on high speed about 8 minutes or until stiff, glossy peaks form (tips stand straight).
Pour hot filling into pastry shell. Immediately spread meringue over hot filling, carefully sealing to edge of pastry to prevent meringue from shrinking. Using a small spoon, swirl meringue to create large peaks.
Bake for 30 minutes. Reduce oven temperature to 275 degrees F. Bake about 50 minutes more or until meringue is golden brown and set when gently shaken.
Cool on a wire rack for 2 hours. Chill for 3 to 6 hours before serving; cover for longer storage. Makes 10 servings.
Baked Deep-Dish Pastry Shell: Preheat oven to 450 degrees F. In a medium bowl, stir together 1-3/4 cups all-purpose flour and 1/2 teaspoon salt. Using a pastry blender, cut in 1/2 cup shortening until pieces are pea-size. Sprinkle 1 tablespoon cold water over part of flour mixture; toss gently with a fork. Push to side of bowl. Repeat with additional cold water, 1 tablespoon at a time (5 to 7 tablespoons total), until all is moistened. Shape into a ball.
On a lightly floured surface, use your hands to slightly flatten dough. Roll dough from center to edge into a 14-inch circle. Wrap pastry circle around rolling pin; transfer to a 9-1/2- to 10-inch deep-dish pie plate. Ease pastry into pie plate without stretching it. Trim pastry to 1/2 inch beyond edge of pie plate. Fold under extra pastry. Crimp edge as desired. Line pastry with a double thickness of foil. Bake for 8 minutes. Remove foil. Bake for 8 to 10 minutes more or until golden brown. Cool on a wire rack.