Pulse the flour, sugar, and salt in a food processor for a few seconds to combine. Scatter the pieces of margarine over the flour mixture and pulse about 15 times until the mixture resembles a coarse yellow meal and no white powdery bits remain.

Turn it out into a large mixing bowl and add the cold water. Fold with a rubber spatula until the dough sticks together.

Divide the dough in two, form into disks, wrap in plastic wrap, and refrigerate for at least one hour or up to one week.

Put the apples and sugar into a large pot and cook, covered, over a medium flame until the liquid is exuded, about 20 minutes. Uncover and cook over high heat until the liquid is mostly boiled out, about five minutes. Cool to room temperature, then refrigerate until cold.

Put the cranberries, sugar, water, salt, and orange zest (if using) into a medium saucepan. Bring to a boil, then simmer until the cranberries burst, 10 to 15 minutes. Cool and refrigerate until firm.

Set the oven rack to the lowest position and place a baking sheet on the rack. Preheat the oven to 425 degrees Fahrenheit.

Select the larger disk of dough (it’s fine if they are the same size—in that case, use either one), sprinkle the top and bottom with flour, and roll it out on a generously floured surface to an 11-inch circle. Transfer the dough to a nine-inch pie plate and trim the overhang to one inch.

Mix the cranberry filling with a fork and spread it on the bottom of the pie crust. Spread the apple filling over the cranberry filling.

Sprinkle the top and bottom of the second disk with flour and roll it out on a generously floured surface to a 10-inch circle. Lay the dough over the filling, fold the overhang over, and crimp to seal.

You can use scraps of dough to make leaves, which you can attach with a bit of water as glue. Brush the beaten egg over the crust, sprinkle the cinnamon sugar over the top, and cut slits to vent.

Place the pie on the baking sheet and bake for 20 minutes. Reduce the heat to 350 degrees Fahrenheit and bake for another hour and a half, until the juices are bubbling. If the top crust browns too much, place a baking sheet on the shelf above the pie to slow the browning.