To make the meat filling:
Cut the meat into large chunks and place in a large, heavy pot. Cover with cold water. Bring to a boil over high heat. Cover the pot, reduce the heat to medium-low, and simmer until the meat is very tender, 2 to 2 ½ hours. Remove the meat and reserve the cooking liquid. When the meat is cool enough to handle, remove and discard any skin and large chunks of fat. Shred or dice the meat into small pieces. There should be 14 to 16 cups of meat. Heat the oil in a large, heavy pot over medium heat. Stir in the chili powder, paprika, salt, onion powder, garlic powder, black pepper, cayenne, and cumin. Add the meat and stir to coat with the oil and spices. Cook, stirring often, until the meat is warmed through, 7 to 10 minutes. Set aside.
To prepare the corn husks: While the meat is cooking, soak the husks in a large bowl or sink of very warm water until they are soft and pliable, about 2 hours. Gently separate the husks into single leaves, trying not to tear them. Wash off any dust and discard any corn silks. Keep any shucks that split to the side, since two small pieces can be overlapped and used as one.
To make the cornmeal dough: Stir the cornmeal, baking powder, salt, and lard together in a large bowl until well blended. Gradually stir in enough warm broth to make soft, spongy dough that is the consistency of thick mashed potatoes. The dough should be quite moist, but not wet. Cover the bowl with a damp cloth.
To assemble the tamales: Remove a corn husk from the water and pat it dry. Lay the husk on a work surface. Spread about ¼ cup of the dough in an even layer across the wide end of the husk to within 1 inch of the edges. Spoon about 1 tablespoon of the meat filling in a line down the center of the dough. Roll the husk so that the dough surrounds the filling and forms a cylinder or package. Fold the bottom under to close the end and complete the package. Place the completed tamales in a single layer on a baking sheet. Repeat until all the dough and filling are used.
To cook the tamales:
To simmer: Stand the tamales upright, closed side down, in a large pot. Place enough tamales in the pot so that they do not fall over or come unrolled. Carefully fill the pot with enough water to come just to the top of the tamales, trying not to pour water directly into the tamales. Bring the water to a boil over high heat. Cover the pot, reduce the heat to medium-low, and simmer until the dough is firm and pulls away from the husk easily and cleanly, about 1 hour.
To steam: Stand the tamales upright, closed side down, in a large steamer basket. Cover the tamales with a damp towel or additional husks. Steam the tamales over simmering water until the dough is firm and pulls away from the husk easily and cleanly, 1 to 1¼ hours.
Serve the tamales warm, in their husks. Remove the husks to eat.
