Place apples in a 12- x 8- x 2- inch baking dish; fill centers of cored apples evenly using 1/2 cup sugar. Pour water into baking dish to a depth of 1/2 inch. Bake at 350° for 45 minutes. Remove from oven; drain off syrup, and discard. Drain baked apples of any excess moisture; return to baking dish. Set aside.
Combine 1/2 c up plus 2 tablespoons sugar and cornstarch in top of a double boiler; stir well. Add milk, mixing well. Set 1 egg white aside in a small mixing bowl. Add egg yolk and beaten eggs to milk mixture; beat well using a wire whisk.
Place over boiling water and cook, stirring constantly with a metal spoon, 20 minutes or until mixture thickens and coats the spoon.
Pour custard evenly around apples in baking dish. Beat reserved egg white (at room temperature) until foamy. Gradually add 1 1/2 teaspoons sugar, beating until soft peaks form. Dollop meringue on top of each apple.
Bake at 350° for 8 minutes or until meringue is lightly browned. Remove from oven, and spoon a baked apple and custard into individual serving bowls. Serve immediately.