Combine peaches and water in a small saucepan; bring to a boil.
Reduce heat and simmer, uncovered, 30 minutes or until tender.
Stir in 1/4 cup sugar; pour into pastry shell.
Combine 3/4 cup sugar and cornstarch in a heavy saucepan.
Gradually add milk, stirring until blended.
Cook over medium heat, stirring constantly, until mixture thickens and comes to a boil; cook 1 minute, stirring constantly.
Remove mixture from heat.
Beat egg yolks until thick and lemon colored.
Gradually stir about one-fourth of hot mixture into yolks; add to remaining hot mixture, stirring constantly.
Cook over medium heat 4 minutes, stirring constantly.
Remove from heat; stir in the butter and vanilla.
Pour over peaches; bake at 350° for 25 minutes.
Beat egg whites (at room temperature) and cream of tartar until foamy.
Gradually add remaining sugar, 1 tablespoon at a time, beating until stiff peaks form.
Spread meringue over hot filling, sealing to edge of pastry.
Bake at 425° for 6 to 8 minutes or until golden brown.
Cool pie to room temperature.