How to Make It
In a large pot, bring 2 quarts of water to a boil. Add the chicken pieces and backbone, onion, garlic and salt and return to a simmer. Cover and cook over low heat until the chicken is white throughout, about 20 minutes. Transfer the chicken to a plate and cover to keep warm. Simmer the broth to concentrate the flavor, about 30 minutes. Strain the broth; discard the solids, including the chicken backbone.
In a large cast-iron skillet, heat 1/4 cup of the lard. Add the chiles and cook over moderate heat, stirring, until toasted, about 2 minutes. Using a slotted spoon, transfer the chiles to a medium saucepan and cover with water. Bring to a boil and simmer until softened, 10 minutes; drain the chiles and transfer to a blender.
Add the tomatoes to the skillet cut side down and cook over moderate heat until lightly caramelized, 3 minutes per side. Transfer to the blender. Wipe out the skillet.
Heat 1 tablespoon of the lard in the skillet. Add the onion and garlic and cook over moderate heat, stirring, until softened and golden, about 5 minutes. Add the chile seeds, raisins, oregano, cumin, thyme, coriander and peppercorns. Cook, stirring, until very fragrant, about 3 minutes. Scrape the mixture into the blender. Add the tomatillos, peanut butter, almond butter, tahini, salt, 1 1/2 tablespoons of the sugar and 1 1/2 cups of water and puree until thick and smooth. Strain the mole sauce into a large bowl.
Wipe out the skillet and heat the remaining 1 tablespoon of lard. Add 2 cups of the mole sauce and 2 cups of the chicken broth (reserve the remaining mole and broth for another use). Bring to a simmer over low heat, whisking constantly. Whisk in the chocolate and the remaining 1 tablespoon of sugar until melted. Cover and cook, whisking, until the mole has thickened and the flavors have melded, about 15 minutes. Add the chicken and cook until warmed through, about 5 minutes. Transfer the chicken and mole to a serving platter and garnish with sesame seeds. Serve warm.