Preheat your oven to 400 F. Skip step #2 below if you're using frozen peaches.
Bring a large stockpot full of water to a boil. Add the peaches and blanch for about 30 seconds, then remove them and dunk them in a large bowl of ice water. After 30 seconds in the ice water, remove the peaches. The skins will now slip right off. Then halve the peaches, remove the pits and slice up the fruit.
In a large mixing bowl, combine the sliced peaches (along with any reserved juices if you're using thawed frozen peaches) with the sugar, cornstarch, cinnamon, nutmeg, salt, and lemon juice. Toss until everything is nicely mixed together. Cover with plastic and let stand at room temperature while you complete the following steps.
Divide the dough in half, and roll each half into a round that's about 1/8 inch thick and 12 inches across. Fit one round over a 9-inch pie tin. Press the dough all the way down firmly without stretching it.
Fill the bottom pie shell with the peach mixture and dot with the cubes of butter.
Brush the edges of the bottom crust with milk to moisten it, which will help get a good seal with the top crust.
Now fit the top crust over the bottom one and press the edges firmly to seal them. Crimp the edges with a fork to trim off the excess dough, or flute the edges with your fingers. Cut a few small slits in the top crust to allow steam to vent.
Brush the top crust with milk and sprinkle with sugar.
Transfer the pie to the oven and bake for about 50 minutes. You can cover the edges with foil if they start to get too dark. The pie is done when the crust is golden brown and flaky and the peach juices are bubbling. Cool on a wire rack for 2 hours before slicing.