In a large bowl, combine sugars; add peaches and toss gently. Cover and let stand for 1 hour. On a lightly floured surface, roll one half of dough to a 1/8-in.-thick circle; transfer to a 9-in. pie plate or iron skillet.Trim even with rim. Refrigerate while preparing filling. , Preheat oven to 400°. Drain peaches, reserving juice. In a small saucepan, combine cornstarch, nutmeg, cinnamon and salt; gradually stir in reserved juice. Bring to a boil; cook and stir until thickened, about 2 minutes. Remove from the heat; stir in lemon juice and butter. Gently fold in peaches. Pour into crust. , Roll remaining dough to a 1/8-in.-thick circle; cut into 1-1/2-in.-wide strips. Arrange over filling in a lattice pattern. Trim and seal strips to edge of bottom crust; flute edge. Cover edge loosely with foil. Bake 40 minutes; remove foil. Bake until crust is golden brown and filling is bubbly, 10-20 minutes longer. Cool on a wire rack. If desired, serve with vanilla ice cream.