Notes: To peel peaches, cut a 1/2-inch X through peel on the bottom of each. Immerse in boiling water until peels pull off easily, 1 to 2 minutes. Transfer peaches to a strainer and rinse under cold running water until cool. Starting at the cut end, slip off and discard peels.
In a large bowl, mix flour, 1 1/2 tablespoons granulated sugar, and salt. Cut 6 tablespoons butter into chunks and, with your fingers or a pastry blender, rub or cut it into flour mixture until coarse crumbs form. Sprinkle 4 tablespoons water evenly over mixture and stir until dough comes together; if necessary, add 1 to 2 more tablespoons water.
Turn dough out onto a lightly floured sheet of waxed paper and pat into a flat disk. With a lightly floured rolling pin, roll into an 11-inch round about 1/4 inch thick. Slide waxed paper onto a 12- by 15-inch baking sheet and chill pastry.
In a large bowl, mix peaches, lemon juice, brown sugar, cornstarch, cinnamon, and nutmeg. Pour into a 9-inch pie pan. Cut remaining tablespoon butter into 1/4-inch chunks and distribute evenly over fruit. Remove pastry round from refrigerator and let stand at room temperature 5 minutes. Slide off waxed paper and center over filling. With a small, sharp knife, trim dough 1/2 inch beyond pan rim. Tuck edges inside rim.
Place pie pan on a 12- by 15-inch baking sheet and bake in a 375° regular or convection oven until pastry is golden, about 30 minutes. Remove from oven and, with a sharp knife, cut crust into 1-inch squares. With the back of a spoon, gently press crust into filling so juice flows over edges of squares. Sprinkle remaining 2 tablespoons granulated sugar over the top, return to oven, and bake until peaches are tender when pierced and juices are thickened, 25 to 30 minutes longer. Serve warm or at room temperature.