Peel, pit and slice peaches. Set aside.
In a saucepan on medium heat, combine granulated sugar, water, cornstarch and lemon juice. Whisk it constantly until it comes to a boil. It will thicken quickly, about 2-3 minutes.
Remove pan from the heat and stir in the peaches. Add the vanilla, cinnamon and nutmeg and stir to combine.
Let the filling cool completely. At that point you can add it to your prepared pie crust.
