To prepare the pork filling, in a heavy 8-quart Dutch oven over medium-high heat, warm the lard. Working in batches, add the pork and cook until well browned, 3 to 4 minutes per side. Transfer to a bowl.

Return all the pork to the pot. Add the onion, garlic, bay leaves, oregano, cloves, chiles, salt, peppercorns and allspice berries plus enough water to cover the ingredients. Bring to a boil, then cover and reduce the heat to a simmer. Cook until the meat is tender and falling apart, 1 to 1 1/2 hours. 

Transfer the pork to a cutting board and let cool briefly, then shred with 2 forks. Strain the broth, discarding the solids, and reserve the broth. Let the broth cool briefly, then skim off the excess fat. NOTE: You will use the broth for the chile sauce and to assemble the tamales.

The recipe may be made to this point up to 2 days ahead. Refrigerate the pork and broth separately.

NOTE: This makes enough chile sauce for 30 pork or chicken tamales.

To prepare the chile sauce, in a 4-quart saucepan over medium heat, warm  1 1/2 tablespoons of the lard. Add the onion and garlic and cook, stirring occasionally, until beginning to brown, about 5 minutes. Transfer the onion and garlic to a blender.

Add the chiles, tomatoes and a little of the broth to the blender and puree until smooth.

In the same saucepan over medium-high heat, warm the remaining 1/2 tablespoon lard. Add the masa harina and cook, stirring, for about 1 minute. Add the chile-tomato mixture and cook, stirring often, until it has darkened in color, 3 to 4 minutes. Add the brown sugar, cumin, oregano, allspice, cloves, 2 1/2 teaspoons salt and enough broth to thin the puree to a sauce-like consistency. Add the cinnamon stick, reduce the heat and simmer, stirring occasionally, until the color deepens slightly, the consistency is smooth, and a light sheen develops on the surface of the sauce, 15 to 20 minutes more, adding more broth as needed. Adjust the seasoning with salt and brown sugar.

Once the sauce is seasoned to your liking, increase the heat to medium-high and bring the chile sauce to a boil; cook until slightly thickened. Season with salt and pepper. Remove from the heat.

For the pork filling: Add the shredded pork to the chile sauce and stir to mix thoroughly. If the pork/sauce mixture becomes too thick, add more broth until the sauce is slightly thickened. Set aside or refrigerate until ready to use.

To prepare the chicken filling, stir the red chile sauce and cook over medium heat, stirring constantly, until thickened, about 5 minutes. Stir in the broth and bring to a boil. Place the chicken thighs in the sauce, reduce the heat to medium, cover and cook until an instant-read thermometer inserted into the thickest part of a thigh registers 175° to 185°F, about 20 minutes. Transfer the chicken to a plate. When cool enough to handle, shred the chicken by hand or with 2 forks.

Increase the heat to medium-high and bring the chile sauce to a boil, then cook until slightly thickened. Remove from the heat and let cool. Season with salt and pepper. 

Add the shredded chicken to the chile sauce and stir to mix thoroughly. If the chicken/sauce mixture becomes too thick, add more broth until the sauce is slightly thickened. Set aside or refrigerate until ready to use.

NOTE: The recipe may be made to this point up to 2 days ahead. Refrigerate the meats separately in the chile sauce until ready to assemble the tamales.

To prepare the masa, in a large bowl, stir together the masa harina and hot water. Cover and let stand at room temperature for at least 30 minutes or refrigerate for up to 2 days.

Using an electric mixer fitted with the paddle attachment or a handheld electric mixer, beat the lard on medium-high speed until fluffy, 1 to 2 minutes. You can also beat the mixture by hand! Add the salt and continue beating while adding the masa in golf-ball-size pieces. When about half of the masa is mixed in, start alternating the masa with the broth until all of the masa is used, along with about 2 cups of the broth. Add 1/4 cup of the chile sauce and beat until light and fluffy, adding more broth if the mixture seems too dry.

To test if the masa is ready, take a small piece (about 1/2 teaspoon) and drop it in a cup of cold water. It should easily float. If not, simply beat the masa for a few minutes more and test again. Don’t add too much liquid or you’ll end up with overly soft masa and shapeless tamales.

Open the packages of corn husks and remove any silk from each husk. Soak the corn husks in very hot water for 10 minutes. Remove the husks from the water and place on a cookie sheet. Cover with a damp towel to keep moist. You’ll have enough husks to make the tamales, plus extra to line the steamer and make up for any broken husks.

To assemble the tamales, wipe a soaked husk dry and place it, smooth side up, on a work surface. Put about 1/3 cup masa in the center of the widest portion of the husk and spread it evenly over one-half to two-thirds of the husk with a spoon or spatula. Leave a 1/2-inch border at each edge.

Put 3 tablespoons of the chile sauce/pork or chicken filling in the center of the masa about 1/2 inch from the wide end.

Fold the corn husk in half lengthwise so the edges meet. Fold the seam back so it’s in the center of the tamale. Fold the tail of the wrapper to cover the seam (at least half the length of the tamale). Make sure there are no holes! Press down slightly on top of the tamale while holding everything in place. The masa will seal the filling like glue. Flip, seam side down, onto a baking sheet. Repeat with the remaining ingredients.

The tamales can be steamed as they are, or tied to make them more secure. For ties, rip long, thin strips off 1 or 2 corn husks. Then place a strip of corn husk under the tamale and wrap it around the middle. Make sure that you have some of the tail underneath and tie securely.

To steam the tamales, use a double steamer or a deep 8-quart pot with a pasta insert with enough water to reach just below the insert. Remove the steamer or insert and bring the water to a boil over high heat. Add more hot water if the water becomes low. 

Stand the tamales upright (open end up) in the insert, leaving room for the steam to circulate. Place the insert into the pot over the boiling water. You can use extra husks to cover the tamales (this also helps to concentrate the heat). Cover the pot with a lid. Steam for 2 hours, adjusting the heat as needed to keep the water just boiling. Check the water level frequently and add more as needed to keep the pot from going dry.

To test for doneness, remove a tamale and replace the lid on the pot. Put the tamale on the counter for a few minutes and then carefully unwrap it. Tamales are ready when the masa is set and pulls easily away from the wrapper.

Remove the tamales from the steamer and let stand for 5 to 10 minutes. Pull off the husk and eat! You can add extra sauce on the side if you like. Tamales may be frozen in plastic bags. To steam frozen tamales, just add 1 hour to the cooking time.