In a large bowl, toss the apples with the sugar, lemon zest and juice, rum (if using), vanilla, cornstarch, nutmeg and salt. Macerate at room temperature for about 2 hours or, refrigerated, overnight.
Preheat the oven to 375 degrees F.
Dust a worktop and rolling pin with flour. Roll out one dough disk a little less than 1/4-inch thick, about 14 inches in diameter. Fold the dough in half and transfer it to a 9- or 10-inch pie plate. Unfold. Press the dough into the corners, leaving the overhang. Refrigerate the first crust while you roll out the second disk of dough.
Remove the bottom crust from the fridge and fill it with the macerated apples. Tuck the pats of cold butter beneath the top layer of fruit. Top with the second piece of dough, and trim both to a 1/2-inch overhang. Tuck the overhang into a roll and crimp the edge, pressing down to hook some of the dough over the edge of the dish. (You want to make a hard crimp because it will shrink as it cooks.) Cut a hole in the center of the pie, as well as some decorative vents.
Brush the top of the pie with cream, dust it with sugar, and bake for 20 minutes.
Then reduce the temperature to 350 degrees F and bake for another 45 to 55 minutes, until the center juices bubble and thicken, for a total of about 1 hour 10 minutes. Let the pie cool until it is just warm to the touch before slicing and serving.
Leaf Lard Crust:
Mix the flour, sugar, and salt in a large bowl. Add the lard and the butter, and cut them in with a pastry blender until the larger pieces are the size of peas and the mixture begins to clump on the pastry blender. Shuffle through the mixture with your hands, pinching chunks of lard to flatten them.
Add 4 tablespoons of the ice water and mix with a fork. Pinch a clump of dough in your hands: If it feels moist and clumps together easily, it's probably hydrated enough. If it feels really crumbly, add another tablespoon or two of ice water until you can form a baseball-size clump of dough, packing it on as if you were making a snowball. You want to mix the dough as little as possible to ensure it stays tender.
Divide the dough in half and form each half into a flat disk. Wrap both disks in plastic wrap and refrigerate for at least 1 hour and up to 2 days.
Thirty minutes before you're ready to roll out the dough, remove it from the refrigerator and let it sit at room temperature to soften.
Adapted from "The New Midwestern Table" by Amy Thielen (c) Clarkson Potter, 2013. Provided courtesy of Amy Thielen. All rights reserved.