Peel and cut the peaches and mix them with the sugar. Let rest in the fridge for at least 30 minutes.
For the dough, place the flour, salt, and cold butter (cut into cubes) in a bowl. With a pastry cutter, cut the butter into the flour until it looks like wet sand, with little flour-covered butter pieces. You can also do this with your hands.
Add the ice water to the flour and mix, first with a spatula and then with your hands, without kneading. Do not add more water since we want a slightly dry dough. Cover in plastic wrap and refrigerate for 45 minutes or until cold.
Meanwhile, prepare the crumble. With a pastry cutter, cut the butter into the flour until a coarse crumble is formed. You can also use your hands for this task. Set aside.
Strain the peach cubes to remove excess liquid. Do not discard the liquid right away, as you’ll need part of it.
Place the strained peach in a saucepan, along with 3 tablespoons of the discarded juice, vanilla, lemon juice, and cornstarch. Bring to medium-low heat, mixing all the time until the filling thickens, approximately 3 minutes.
Roll the dough and press it into a 9-inch pie pan. Tuck in the excess dough to the sides of the pan, and pinch it to make a nice border.
Pour the filling over the dough and spread with a spatula.
Place the crumble over the filling. Place the pan on a baking tray lined with parchment paper.
Bake in a preheated oven at 375°F (190°C) for 1 hour and 10-15 minutes, until the crumble and the edges of the pie are golden brown.
Let cool for at least 3 hours and unmold.
Serve with a scoop of ice cream or cream.