Put the lard in the bowl of a mixer and beat on medium speed until light and fluffy, 5 minutes. Add the masa harina and beat for 2 minutes more. Add the baking powder and salt and continue to beat until incorporated, about 5 minutes. Add the broth and continue to beat until the masa is soft and fluffy (the masa should come off the bowl easily). Set aside, cover with a damp towel and let rest for about 10 minutes, or until ready to use.
Put the corn husks in a large pot, cover with water and bring to a boil. Simmer, uncovered, until soft, about 8 minutes. Drain.
To fill the tamales: Holding an open softened corn husk in one hand, spread about 2 tablespoons of the dough on the husk beginning 1 inch from the wider top and ending at least 1 1/2 inches from the narrower bottom, leaving a 1 1/2-inch border on either side. Sprinkle about 1 tablespoon of filling down the center of each tamal. Fold the sides of the husk up and over the filling, tucking the ends under. Continue with the remaining dough.
Put the folded tamales in the steamer basket of a large pot. Add enough water to cover the bottom of the pot by several inches, but not enough to touch the tamales themselves. Bring to a boil, cover with a towel and lid and steam over medium-low heat for 1 hour, adding additional water to the pot as necessary; do not allow the pot to boil dry. Open a tamal and check for doneness; the tamal should be firm and pull away from the husk without sticking. If still sticky, continue steaming until done, up to another 15 minutes.
Char the poblanos directly over a gas flame on the stove or under the broiler until blackened on all sides. Enclose in a plastic bag and let steam for about 10 minutes.
Peel, stem, seed and devein the chiles. Slice into 1/4-inch strips lengthwise and season with salt. Place 2 to 3 rajas (pepper strips) and 1 tablespoon shredded cheese in each tamal.
For the guajillo chicken filling: Put the chicken, 3 cloves of the garlic, the halved onion and the bay leaves in a large heavy saucepot and add enough water to cover the chicken. Bring to a boil and reduce to a simmer. Simmer for 15 minutes, then skim and cover the pot. Continue to simmer until the chicken is fully cooked, 30 more minutes. Set aside until the chicken is cool enough to handle.
Add the chiles, remaining 4 cloves garlic and the quartered onion to a pot with 4 cups of water. Bring to a boil and remove from the heat. Transfer the ingredients to a blender. Add the cumin and cloves and process until smooth.
Heat the vegetable oil over medium-high heat in a large heavy saucepot. Transfer the chile mixture to the pot and bring to a boil. Reduce to a simmer and simmer for 15 minutes.
Shred the chicken, discarding the bones and excess fat. (Reserve the cooking liquid for another use.) Transfer the shredded chicken into the simmering salsa. Cook until reduced by two-thirds and the flavors are incorporated, about 15 minutes. Season with salt and pepper.
When blending hot liquids, first let cool for 5 minutes or so, then transfer to a blender, filling only halfway. Put the lid on, leaving one corner open; this will prevent the vacuum effect that creates heat explosions. Cover the lid with a kitchen towel to catch splatters and pulse until smooth.