Peel, core and cut the apples into 1/4-inch slices. Toss the slices in a bowl with the lemon juice and zest to keep them from browning. In another bowl, whisk together the flour, brown sugar, cinnamon and salt. Sprinkle this over the apples and toss until the fruit is evenly coated.
Melt the butter in a large, heavy-bottomed pot. Add the apple mixture and saute for 5 minutes. Add the cream and vanilla and continue to cook the apples, stirring often, until the juices thicken and the apples are just tender, 5 to 10 minutes more (see Cook's Note). Set aside to cool completely, about 30 minutes.
Roll out one-third of the tripled pie dough into a large (about 14-by-19-inch) rectangle. Wrap the dough loosely around the rolling pin and transfer it to a half-sheet pan, gently pressing it into the edges and corners of the pan. Prick the bottom of the dough all over with a fork, then refrigerate.
Roll the remaining two batches of dough into one large, rough 1/4-inch-thick rectangle. Slice into lattice strips. (You can cut them all even thickness or alternate between thick and thin strips. I cut 1 1/4-inch strips and 1/2-inch strips.) Gather any dough scraps, wrap them in plastic wrap and refrigerate.
Build the lattice on a sheet of parchment set on the back side of a half-sheet pan sprinkled with flour. Start by laying strips crosswise about 1/2 inch apart. Gently fold every other strip halfway over. Place a strip lengthwise on the parchment and fold the shorter strips back over. Fold up the opposite strips you just used and place another strip lengthwise; fold the short strips back over. Repeat on both sides until you have a basket weave pattern. Roll out any remaining dough scraps and use cookie cutters to cut leaf or flower shapes. Place the lattice and sheet pan in the freezer while the filling cools.
Assembly: Preheat the oven to 350 degrees F. Spoon the cooled filling onto the bottom crust in an even layer. Slide the chilled lattice top onto the bottom crust, using the parchment to help. With a sharp knife, cut the lattice flush with the edges of the pan. Use egg wash to adhere any cut-outs to the top of the pie. Brush egg wash over the crust and sprinkle with sanding sugar.
Bake until the filling is bubbling in the center and the top and bottom crusts are golden brown, 45 to 50 minutes.
In the bowl of a food processor fitted with the blade attachment, pulse together the flour, salt, sugar and butter until the mixture resembles cornmeal with some pea-size pieces of butter remaining.
In a small bowl, stir together the ice water and the lemon juice. Slowly add the liquid to the flour mixture, pulsing, until the dough just comes together. Squeeze a small piece of dough between your thumb and index finger to make sure it holds its shape.
Turn the dough out onto a lightly floured surface and gently turn it over each a few times so that any dry bits are incorporated. Form into a disk or rectangle, wrap in plastic and refrigerate for at least 20 minutes.
Adapted from "Pie It Forward: Pies, Tarts, Tortes, Galettes, and Other Pastries Reinvented" by Gesine Bullock-Prado © Stewart, Tabori & Chang 2012. Provided courtesy of Gesine Bullock-Prado. All rights reserved.
Make sure not to overcook the apples or they will become mushy. If the juices haven't thickened by the time the apples are tender, transfer the cooked apples to a large bowl and continue to cook the juices. Once they've thickened, add them to the apples.