Fresh Peach Pie

I adapted this recipe from one on Allrecipes.com. I love it because it doesn't use any artificial glaze and I love the freshness of the peaches.

1 (9 inch) pie shell, baked
3/4 cup white sugar
1/3 cup water
2 tablespoons cornstarch
2 tsp butter
1 1/2 cups fresh peaches, pitted and mashed
1/4 teaspoon ground nutmeg
1 teaspoon vanilla extract
4 1/2 cups fresh peaches - pitted, skinned, and sliced

Combine sugar, water, cornstarch, butter or margarine, mashed peaches, and nutmeg in a saucepan. Cook over medium heat until clear and thick. Stir in vanilla. Fill pie shell with half of the sliced peaches, then half of the glaze, then the rest of the peaches and glaze. Refrigerate until cold, then serve.