Combine flour, salt, and cold butter in a food processor. Pulse until you have small butter grains. Pour mixture into a separate bowl and add cold water. Mix with your hands until you can form a ball. Wrap the dough ball in plastic wrap and flatten into a disc. Chill in the fridge for an hour.
Make filling by tossing together peaches, brown sugar, lemon juice, cornstarch, and salt. Mix until cornstarch is dissolved.