Lightly flour your work surface and roll one disc of dough into a 12 inch circle. Fit it into a 9" pie plate and let the excess hang over the sides. Loosely cover with plastic wrap and refrigerate for 30 minutes -- until dough is firm.
Roll out the other disc of dough into a rectangle, roughly 12" x 10". Trim rounded edges and use a ruler to score and slice into even 10" long strips, each about 1" wide. Separate the strips on a cookie sheet and freeze until firm, about 30 minutes.
Transfer peaches and sugar into a large bowl and toss until peaches are well coated. Let sit for an hour, so the peach releases it's juices.
Preheat oven to 425 degrees. Adjust oven rack to the lowest point in your oven. Line a rimmed baking sheet with aluminum foil.
Place a strainer over a medium bowl. Transfer the peaches to the strainer to drain the juices. Reserve 1/4 cup of the juices for the pie. (Reserve the rest of the juices for an outstanding cocktail on the blog later this week).
Transfer peaches back to the original bowl and add the cornstarch, lemon juice, cinnamon, nutmeg and salt. Toss until well combined.
Spread peaches into the pie crust. Lay 5 strips of pie crust evenly across the peaches parallel to one another. Weave remaining strips perpendicular to the first ones, to create a lattice crust. Any excess or hanging dough should be tucked under on itself. Press your thumb and forefinger together and gently place it on the rim of the dough. Use the knuckle on your other hand to crimp the dough. Continue around the circumference of the pie. Place the pie on the baking sheet. Brush the lattice work and crust with cream, then sprinkle the demerara sugar on top.
Mold the tin foil around the perimeter of the pie. Bake for 25 minutes, then turn down the oven to 375 degrees. Rotate the pan halfway to promote even cooking. Cook for an additional 30 minutes, then remove the tin foil. Cook an additional 10-15 minutes.
Cool the pie on a rack until filling has set, about 2 hours. Best served warm or at room temperature.