To the bowl of a food processor or a large mixing bowl, add flour, sugar, and salt. Pulse a few times or whisk to combine. Add butter and pulse until dough is crumbly and butter is in pea-sized pieces; or use a pastry blender or two knives to cut butter into flour. Add half the ice water and pulse or stir to combine. Add remaining water a little at a time until dough just comes together in a shaggy ball. Remove dough to a work surface and knead very lightly just until dough forms a smooth ball. Divide in half, flatten into discs, wrap in plastic wrap, and chill at least 1 hour or overnight.
Have ready a 9 or 10” pie dish or cast iron skillet. Lightly flour a work surface and place half of chilled dough on it. Roll out dough, applying even pressure with a rolling pin, into a circle 2 inches larger than the pie dish. If dough cracks, let it warm up for a few minutes before continuing. Patch any holes or large cracks with excess dough. Loosely roll dough around rolling pin and transfer to pie dish. Trim edges of dough to have a ¾” overhang. Poke dough all over with a fork, and chill 30 minutes. Place second dough round on work surface and roll out as above. Cut dough into ¾” strips. Place half the dough strips 1-2” apart on a lightly floured cookie sheet, then weave remaining dough strips through them in a basket-weave pattern. Chill lattice 30 minutes.
Bring a large pot of water to a boil and prepare an ice water bath. With a paring knife, score the bottom of each peach with an X. With a slotted spoon, carefully lower peaches into water and blanch 2-3 minutes. Remove to ice water bath to cool. Peel skins off peaches with a paring knife and cut into ½” slices.
Preheat oven to 400˚F. In a large mixing bowl, combine peaches, cherries, 1 cup sugar, cornstarch, lemon juice and cinnamon. Pour into chilled pie shell. Slide lattice crust off cookie sheet on top of filled pie shell. If lattice and crust are very cold and brittle, let warm up for a few minutes. Fold overhanging dough of bottom crust over edges of lattice. Crimp edges or press with the tines of a fork. Brush lattice with egg wash and sprinkle with remaining 2 tablespoons sugar. Bake 30 minutes, then reduce oven temperature to 350˚F and bake 30-40 minutes more, or until browned and bubbly. Remove to a rack and cool 1 hour.