Preheat the oven to 425 degrees F.
In a large mixing bowl, combine the flour and salt. Add the Crisco or cold butter and work it in with your fingers until the mixture resembles coarse meal.
Make a well in the center and add the cold water. Gently bring the flour mixture into the water until the dough is just combined and evenly moistened. Do not overmix or knead.
Form the dough into a flat disc, wrap in plastic, and chill for 30 minutes to 1 hour.
Roll the chilled dough on a lightly floured surface into a circle about 1/4 inch thick and large enough to overhang a 9-inch pie plate by at least 1/2 inch.
Fit the dough into the pie plate, press it gently into the sides, fold the edges under, and pinch to form a decorative edge.
Prick the bottom and sides of the crust with a fork about every 2 inches. Line with parchment paper or foil and fill with pie weights or dry beans.
Bake for 12 to 15 minutes, until the edges are lightly golden. Remove the weights and parchment, then let the crust cool.
Add the peeled and sliced peaches to a medium bowl and sprinkle with sugar. Let them sit at room temperature for 30 minutes, then drain and reserve the juices.
Pour the reserved peach juices into a measuring cup. Add lemon juice and enough water, apple juice, or white grape juice to equal 1 cup of liquid.
Transfer the liquid to a medium saucepan. Add cornstarch and salt, then whisk until smooth.
Cook over medium heat, whisking constantly, until the mixture bubbles and thickens. Boil for 30 seconds.
Remove from the heat and stir in the butter and almond extract until smooth. Let the glaze cool to room temperature.
Fold the cooled glaze gently into the sliced peaches, then spoon the peach mixture into the cooled baked pie crust and spread evenly.
Cover with plastic wrap and chill for at least 1 hour, or up to 24 hours before serving.
