To prepare the dough, place the flour, sugar and salt in a food processor. Pulse the dry ingredients several times to mix.
Add the butter and pulse the machine until the mixture looks like coarse cornmeal (a few larger pieces of butter are fine).
With the machine running, add the water and mix until the dough just begins to come together. It will still be very crumbly but should form dough when pressed together.
Divide the dough into 1/3 and 2/3 portions, wrap in plastic wrap and flatten into round discs. Place in the refrigerator for a minimum of 1 hour (up to 48 hours).
Prepare the filling:
Bring a large pot of water to a boil. Fill a separate large bowl with ice water. On the bottom of each nectarine, slice a 1-inch X shape (the goal is to cut the skin, not the fruit). Using a slotted spoon, carefully add a few of the nectarines to the boiling water. After 30 seconds to 1 minute you should see the skin separating slightly from the fruit. Use the slotted spoon to move the nectarines into the ice water bath. Repeat with the remaining nectarines.
Peel the skin from the nectarines (discard the skins). If any of the skins are stubborn, use a small paring knife to assist in the peeling. Slice the fruit in half and remove the pits. Place the nectarines flat side down and cut into thin slices. Place the sliced nectarines in a large bowl and toss with the lemon juice.
In a small bowl, stir together the sugars, cinnamon, nutmeg, salt and cornstarch. Add to the nectarines, stirring to combine. Set aside.
Assemble the pie:
Preheat the oven to 425 degrees F.
On a generously floured surface, roll out the larger portion of dough to about 12-13 inches in diameter (flour the top of the dough as well). Carefully place in a 9 1/2 inch pie pan. There should be a slight overhang. Add the nectarine filling.
Re-flour the surface and roll out the smaller portion of dough to approximately 10 inches in diameter. Use a pizza slicer to cut 8 even strips. Layer the strips in a decorative lattice pattern. Cut off any excess overhang from the strips and then fold the bottom overhang over the strips. Use a fork to gently crimp the edge of the crust all around.
Brush the milk or cream evenly over the dough and sprinkle with the turbinado sugar (this will add a nice crunch).
Place the pie pan on a baking sheet and place in the oven. Cook for 20 minutes and then lower the oven temperature to 375 degrees F. Bake for an additional 35-40 minutes, or until the crust is brown and the filling is bubbly.
Allow to cool completely to room temperature before slicing (the filling will thicken as it cools).