For the crust: Combine the flour, granulated sugar and salt in a food processor and mix until combined. Add the butter and pulse until evenly combined and the size of small pebbles. Pour in the vinegar and pulse 1 to 2 times until just combined. With the food processor running, slowly pour in the cold water, adding just enough for the dough to form a ball. You may not need the entire 1/3 cup of water.
Remove the dough from the food processor and form it into a ball. Cut off about a third of the ball so you have a small piece (about 10 ounces) and a larger piece (about 1 pound 6 ounces; see Cook's Note). Form both pieces of dough into discs, wrap in plastic wrap and refrigerate for at least 4 hours.
Preheat the oven to 400 degrees F. Spray a baking sheet very lightly with cooking spray.
Dust a work surface lightly with flour. Roll the larger disc of dough into a rectangle that is 2 inches larger on all sides than the baking sheet. Roll the dough onto the rolling pin and then unfold it over the baking sheet, gently guiding the dough into the baking sheet and lightly pressing it into the corners, sides and bottom. Refrigerate while you prepare the rest of the pie.
Lightly dust the work surface with flour and roll out the smaller disc of dough into a 20-by-12-inch rectangle. Place a ruler along the 12-inch side of the dough and make a mark with a pizza cutter every 1/2 inch. Turn the ruler along each mark and use it as a guide to cut a straight line, making twelve 1/2-inch strips that are 20 inches long. Transfer the strips of dough to a baking sheet, laying them diagonally so they fit and dusting the strips with flour as you lay them down. Refrigerate while you make the filling so the dough does not begin to stick together.
For the filling: In a large bowl, mix together the plums, granulated sugar, cornstarch, almond extract, orange zest and juice, cinnamon, ginger and salt, making sure the plums are evenly coated. Let sit no more than 5 minutes.
To assemble: Evenly spread the filling over the crust on the baking sheet. Lay one of the dough strips diagonally across the baking sheet from one corner to the other. Repeat laying strips parallel to the first piece evenly across the rest of the pie. You can cut strips down to size as you work your way towards the end of the pie, making sure to leave a bit of overhang on both sides.
Take every other strip of dough and fold it back over itself so that it exposes a little more than half of the filling. Lay a long strip of dough in the opposite direction, going diagonally from one corner to the other. Fold the dough strips back down and you will begin to see a lattice form. Fold back every other strip of dough that you didn't fold back before, and then lay another strip of dough diagonally across the pie, working towards a corner. Continue this process until half the pie has a lattice top. Then rotate the pan and repeat the same process on the other side to finish the lattice.
Fold the dough hanging over the sides of the pie up and over the edge, tucking the ends of the strips from the lattice top inside. This will ensure the strips of dough stay anchored to the edges of the pie. Crimp the edges of the dough using your pointer fingers and thumb to pinch the dough together.
Whisk together the heavy cream and egg and brush evenly over the lattice top and edges of the pie. Sprinkle the entire pie with turbinado sugar and bake until the crust is a deep golden brown and bubbles form towards the middle of the pie, about 1 hour and 10 minutes. Let cool completely, at least 40 minutes.
The weights for dividing the dough are approximations, which depend on your climate and how much water you add to the dough. It is most important to divide the dough so you have 1 piece that is twice the size as the other piece of dough.