Make a batch of pie dough. My recipes for all-butter and butter-and-leaf-lard dough make enough for two big disks of dough. Wrap one and freeze it for later. Put the other in the refrigerator for an hour or so. Prepare a large bowl of ice water. Have it near the stove.
Fill a 6-quart soup pot half-full with water and put it on high heat. When the water gives off steam, turn off the heat. Using a large slotted spoon, gently lower the peaches into the water. Leave them there only 15 seconds. Lift them out again and place them in the ice water. After a few minutes, take them out and put them on a cutting board.
Once the peaches have cooled to room temperature, cut them in half and remove the pits. Peel each half, and cut it into four or five thick slices. Put the peach slices in a large bowl.
In a small saucepan on the stove, combine 1/2 cup water with 1/3 cup sugar over medium-high heat. Stir until sugar is dissolved. Add one cup of the peach slices.
In a small bowl, combine the remaining 2 Tbsp. water with the 2 Tbsp. cornstarch. Stir til blended.
Bring the sugar-water-peach mixture to a boil. Turn heat down to medium and simmer for 30 seconds.
Add the cornstarch-water mix, taking care to stir constantly while you’re pouring it in so no lumps form. Add the salt. Cook 1-2 minutes more, until the mixture thickens. Set aside to cool slightly.
When the glaze is still quite warm, but not hot, pour it over the peaches and stir just enough to mix. Pour the filling into the baked crust.