Make the Crust: In a food processor, pulse the flour, sugar and salt together to combine. Add the butter and pulse until the mixture resembles coarse meal, with a few pea-size pieces of butter remaining, about 5 pulses. Sprinkle 3 tablespoons of the ice water over the mixture and pulse until the dough is crumbly but holds together when squeezed, about 5 to 10 pulses. If necessary, add up to 2 tablespoons additional ice water, 1 tablespoon at a time; do no overmix. Form the dough into a disk and wrap tightly in plastic wrap. Refrigerate until firm, at least 1 hour, or overnight.
Make the Crumble: In a small bowl, combine the flour, brown sugar and oats; using your hands, work in the butter until large clumps form. Cover the bowl with plastic wrap and refrigerate until ready to use.
Preheat oven to 375 degrees F. Lightly flour a work surface and rolling pin and roll dough out into a 12-inch circle. Transfer to a 9-inch pie plate, fold the overhanging dough underneath itself and crimp the edges. Place the dough-lined pie plate in the refrigerator while the filling and crumb topping is prepared.
Make the Filling: In a large bowl, toss together the sliced peaches, flour and brown sugar until combined; set aside.
Assemble and Bake the Pie: Transfer the peaches to the pie shell, then break the crumble into medium to large size pieces and sprinkle evenly over the top of the pie. Place the pie on a rimmed baking sheet and bake until the juices are bubbling and the topping is golden, 1 hour to 1 hour 15 minutes. Let cool on a wire rack at least 1½ hours before serving. The pie can be stored, covered at room temperature, for up to 2 days, but it is best eaten the day it is made.