2 3/4 pounds (about 8 medium; 6 cups sliced) peaches, peeled, pitted and cut into 16 slices each
1 tablespoon freshly squeezed lemon juice
1/2 cup plus 1 tablespoon sugar (4 ounces)
Flaky Cream Cheese Pie Crust recipe, for a 9-inch, 2-crust pie (see related recipe)
Flour, for dusting the work surface
4 teaspoons cornstarch (about .5 ounce)
1/2 teaspoon pure almond extract
Place the sliced peaches in a large bowl. Sprinkle them with the lemon juice, then the sugar and salt; toss to coat evenly. Let them sit at room temperature for at least 30 minutes and up to 1 hour.
Place a colander over a small saucepan; transfer the peaches and any collected liquid to the colander. Almost 1 cup of liquid should be captured in the saucepan. Place the saucepan over medium-high heat; cook for about 12 minutes, or until the juices have been reduced to a syrupy 1/3 cup.
Twenty minutes before you are ready to bake, preheat the oven to 425 degrees. Remove the pie plate with the (unbaked) bottom crust from the refrigerator; discard the plastic wrap.
Ten minutes before assembling the pie, remove the second disk of pie crust dough from the refrigerator.
Cover the work surface with a large pastry cloth and lightly dust with flour. Cover a rolling pin, preferably chilled or cool, with a cloth cover and roll the dough into a circle about 1/8 inch thick by 12 inches in diameter. (Alternatively, roll the dough between 2 large sheets of plastic wrap.) The dough should be smooth and cool.
Return the peaches to the large bowl and add the cornstarch and almond extract; toss gently to coat until all traces of the cornstarch disappear.
Pour the reduced syrup over the peaches and toss gently; do not worry if it hardens on contact with the fruit. It will dissolve during baking. Pour the peach mixture into the pie shell.
Use a little water to wet the rim of the bottom crust. Carefully fold the top-crust dough in half, and then again into quarters; transfer to the filled bottom crust and gently unfold on top of the peaches. Tuck the overhang under the bottom crust edge and press down all around the top to seal it. Crimp the edges in a decorative fashion and cut four 3-inch slits in the crust to vent steam.
Create a protective shield for the edge of the pie crust (to prevent overbrowning) by lightly crimping a ring of aluminum foil over it. Place the pie on the floor of the oven to bake for 20 minutes, then transfer to a baking sheet lined with parchment paper. Adjust an oven rack so it is on the lowest level in the oven, place the baking sheet with pie on that rack and bake for 40 to 50 minutes, until the juices bubble thickly through the slits in the top crust and the peaches feel tender but not mushy.
Transfer to a wire rack to cool for at least 3 hours before cutting (the pie will still be warm after 4 hours).