Step 1

Bring salt and 4 cups water to a boil in a 16-qt. pot, stirring until salt is dissolved. Remove from heat and add onion, garlic, thyme, bay leaves, cinnamon sticks, and marinade to pot. Chill, uncovered, until cold, about 1 hour.

Step 2

Add 6 quarts cold water to pot and carefully lower in turkey. Place a heavy plate on top of turkey to keep it submerged. Cover and chill at least 12 hours and up to 1 day. (The turkey will be more moist and flavorful if you let it brine the full time.)

Step 3

Mix flour and salt in a large bowl with a fork to combine. Add shortening and butter and toss to evenly coat. Working quickly and aggressively and using a pastry blender or 2 forks, press into dry ingredients until pieces of butter and shortening are about the size of a dime (the idea is to smash the butter into the flour, creating some pieces that are flat and thin and some that are large and chunky). Drizzle 1 Tbsp. ice water over mixture and stir in with a fork. Knead dough gently in bowl until it comes together (it will still look a little dry).

Step 4

Turn dough out onto a work surface and knead 1 or 2 more times, pressing to incorporate shaggy edges. Press into a disk about 1" thick and wrap in plastic. Chill at least 1 hour.

Step 5

Do ahead: Dough can be made 1 day ahead. Keep chilled, or freeze up to 1 month.

Step 6

Place potatoes in a large saucepan and pour in water to cover by at least 2"; season generously with salt. Bring to a boil, reduce heat, and simmer until a paring knife easily slides through flesh, 25–35 minutes. Drain potatoes and let cool slightly.

Step 7

Meanwhile, bring half-and-half and butter to a simmer in a small saucepan over medium heat.

Step 8

Cut potatoes in half lengthwise. Pass potatoes through a ricer or food mill into a large bowl. (If you don’t have either, gently mash in bowl with a potato masher.) Pour in half-and-half mixture and mix well. Stir in thyme and lime zest; season with pepper. Set aside.

Step 9

Do ahead: Potatoes (without thyme, zest, and pepper) can be made 1 day ahead. Let cool; cover and chill.

Step 10

Line a large rimmed baking sheet with 3 layers of foil; set a wire rack inside. Remove turkey from brine and transfer to a plastic cutting board; discard brine. Pat turkey dry inside and out. Place, breast side up, on rack and tuck wings underneath. Let sit at room temperature 1 hour.

Step 11

Purée chiles, cloves, and 1 cup jerk seasoning in a blender. Transfer chile mixture to a small bowl; set aside.

Step 12

Melt butter in a small saucepan over medium heat. Add remaining ¼ cup jerk seasoning and whisk until smooth, about 1 minute. Remove from heat.

Step 13

Place a rack in middle of oven; preheat to 450°. Wearing disposable food-grade gloves to protect your hands from chiles, gently separate skin from breast meat starting at neck. Spread chile mixture over breast meat underneath skin, then smear remaining chile mixture all over outside of turkey. Tie legs together with kitchen twine and pour 1 cup broth into baking sheet.

Step 14

Roast turkey, rotating pan halfway through, until skin is mostly golden brown, about 30 minutes. Reduce oven temperature to 300° and continue to roast, brushing with jerk butter every 30 minutes and adding ½ cup broth to pan if liquid evaporates, until an instant-read thermometer inserted into the thickest part of breast registers 150°, 65–85 minutes longer. Skin should be deep golden brown and lacquered-looking. Transfer turkey to a cutting board; let rest 2 hours. Pour juices from pan into a heatproof measuring glass.

Step 15

Let dough sit at room temperature 5 minutes. Roll out on a lightly floured surface to a 10½"–12" round (1½"–2" wider than pan). Place dough in a 9"-diameter pie pan or 10" cast-iron skillet; lift up edges, allowing dough to slump down into skillet. Trim any overhang and crimp edges as desired. Chill until ready to use.

Step 16

Carve turkey and shred meat. Measure out 5 cups (a mix of light and dark meat is good); save remaining meat for other uses. Arrange meat evenly in dough. Pour just enough pan juices over turkey to moisten (be careful not to oversaturate or your crust may be soggy). Mound potatoes over meat. Using a wet butter knife or spoon, spread to edges, covering meat completely. Using a fork, create decorative ridges in potatoes and sprinkle with paprika. Brush dough with half-and-half. Bake pie until crust is golden brown, 35–45 minutes. Let cool 15 minutes. Serve with cranberry sauce.