For the filling: Peel peaches if desired. Remove stone and slice to desired thickness (I do about 1/2-inch); set aside.
Mix sugar, salt and cornstarch together in a large saucepan. Gradually add the water, whisking so there's no lumps. Heat over medium heat, stirring constantly, until mixture boils. While still stirring, reduce heat to low and cook for about 5 minutes. Add the peaches and mix well. Let this cool to room temperature
For the crust: Measure the flour and butter into a food processor and blend until the mixture resembles breadcrumbs. Add the egg and water and blend again until it forms a smooth dough ball. Roll on a lightly floured work surface/ Slip the removable bottom of a deep 8-10-inch tart/quiche pan (available in my Amazon store) in the center of the rolled dough. Fold overhanging dough towards the center of circle (like a galette). Place the pan bottom with the dough into the ring of the tart pan; unfold the overhang and press into the fluted sides. Refrigerate for 15 minutes.
For the crumbs: Melt butter in a small saucepan. Add the brown sugar and stir to combine. Add the flour gradually, mixing in until you get a mixture that holds together when pressed. You may need more flour. If you do, add it a tablespoon at a time until you get a mixture where the crumb will hold it's shape.
Preheat oven to 375 degrees Fill pastry shell with the peach filling. Top with the crumbs. Place the tart pan on a parchment-lined baking sheet. Bake 40-45 minutes or until crumbs are browned and filling bubbles up around the edges.