Preheat your oven to 375°F (190°C).
In a mixing bowl, combine flour and cold, cubed butter. Mix until the mixture resembles coarse crumbs.
Add ice water, a tablespoon at a time, until the dough comes together. Divide the dough into two discs, wrap in plastic wrap, and refrigerate for at least 30 minutes.
In another bowl, combine thawed peaches, sugar, cornstarch, cinnamon, nutmeg, and lemon juice. Mix well.
Roll out one disc of dough and fit it into a pie dish. Pour the peach filling into the crust.
Roll out the second disc of dough and place it over the filling. Trim and crimp the edges, and cut a few slits in the top crust to allow steam to escape.
Bake for 45 minutes or until the crust is golden brown and the filling is bubbly. Let cool before serving.