Make dough: In bowl of food processor, add 1 ¼ cups flour, butter, and salt. Pulse until combined; some pieces of butter should still be visible. Through feeder tube, add ice water about 1 tablespoon at a time and continue pulsing until dough turns into ball in food processor. Remove from food processor and form dough into round disc. Wrap in parchment paper or plastic wrap; place in refrigerator until chilled, 20 to 30 minutes.
Preheat oven to 425 degrees F. Meanwhile, prepare peaches, then add to medium bowl with brown sugar, vanilla, cinnamon, lemon zest, lemon juice, and remaining 1 tablespoon flour. Let sit for juices to accumulate.
When dough is chilled, place on lightly floured surface. Using rolling pin, roll into 12-inch circle.
Transfer dough onto parchment-paper-lined baking sheet. Scatter peaches over dough, leaving 2-inch border around edge of crostata. Fold border over top of peaches to form crostata. If desired, whisk egg white and water in small bowl and brush mixture over crostata crust, then sprinkle crust with granulated sugar.
Cook in oven until crust and peaches are cooked, about 30 minutes. Remove from oven and let cool slightly before cutting. Serve.