Preheat the oven to 400 degrees F. Line a large baking sheet with parchment paper or foil.
Stir together the peaches, brown sugar, flour, cinnamon, nutmeg, and lemon juice in a large bowl until combined.
On a well-floured surface, using a lightly floured rolling pin, roll out the pie dough into a large circle, about 12 to 14 inches in diameter. Move the dough circle to the prepared baking sheet. Chill the rolled-out dough in the refrigerator until firm, about 15 minutes. Spoon the fruit mixture onto the center of the dough leaving a 1-inch border. Fold the edges of the dough over the fruit, pleating the dough, then dot the fruit filling with the butter pieces. Lightly brush the dough with the beaten egg, and sprinkle with sugar.
Bake the pie until the crust is golden brown and the filling is bubbling, 25 to 30 minutes. Cover if the crust browns too quickly. Allow the pie to cool slightly. Serve warm with vanilla bean ice cream or alongside fresh whipped cream.
In a mixing bowl, mix together the flour and the salt; cut or work the butter into the flour with your fingers or with a pastry blender until you have large pea-size chunks scattered throughout. Alternatively, pulse the dough in a food processor, or mix in a stand mixer with the paddle attachment on low speed.
Add the ice water slowly while stirring with a fork, or in the food processor or mixer, until just combined. Be careful not to overwork the dough. Divide the dough into 2 disks, flatten and refrigerate each for at least 15 minutes.
The same recipe can be made in individual serving sizes. Pate Sucree (sweet dough): Add 3 tablespoons sugar and 1/2 teaspoon pure vanilla extract to the original recipe. Savory Dough: Add 1/4 cup grated cheese to the original recipe. Nutty Dough: Reduce the flour to 1 cup and add 1/2 cup roasted pulverized nuts. (recommended: almonds, pecans, walnuts, etc.) Blind Baking (Method): Roll out the chilled pie dough to fit a 9-inch pie plate. Transfer the dough to the pie plate pressing the dough lightly into the plate and then trim the edges. Dock the dough with the tongs of a fork evenly over the bottom of the pie plate. Line the docked dough with aluminum foil and fill with pie weights or dried beans. Bake the pie crust in a 425 degree F oven until the edges are brown and golden. Bake 15 minutes with pie weights. Remove the crust from the oven and remove the pie weights. Return the crust to the oven to finish baking for another 5 minutes.