Preheat the oven to 400°F (207°C).
Using a stand mixer with a paddle attachment, mix the flour, salt, and butter on low speed for 2 minutes. Slowly add ice water until the dough forms a ball.
Transfer the dough to a lightly floured work surface and knead it 2 or 3 times, just until it comes together. Pat the dough into a disk. On the floured surface, roll out the dough into a 16- to 17-inch (40 cm to 43 cm) round, about 1/4 inch (5 mm) thick. Line a large baking sheet with parchment paper. Roll the dough around the rolling pin and transfer it onto the prepared baking sheet.
Peach Filling: Wash the peaches and, if needed, rub them to remove any fuzz. Cut the peaches in half, remove the pits, and slice them into thick 1-inch (2.5 cm) pieces. Place the peach slices in a large bowl and season with salt. Then, add 3 tablespoons of sugar and gently toss to combine.
Arrange the peach slices on the pastry, placing them as close together as possible without overlapping too much. Leave about a 2-inch wide border around the outside. Gently fold the edges of the pastry up and over the peaches, pleating as necessary. Be sure to seal any cracks in the pastry.
Bake the tart in the center of the oven for 1 hour, or until the peaches are tender and golden and the crust is cooked through. Let the tart cool slightly before serving. Optionally, dust with powdered sugar.