Heat 1 tablespoon of the lard in a large skillet over medium heat. Quickly fry the ancho, mulato, and pasilla chiles for 2–3 seconds per side until fragrant. Transfer them to a bowl, cover with hot water, and soak for 20 minutes.
Char the Roma tomatoes in a dry skillet until blackened in spots. In the same skillet, cook the onion and garlic until softened and lightly browned.
Toast the almonds until fragrant, about 2 minutes. Toast the sesame seeds separately until lightly golden and reserve 1 tablespoon for garnish.
Toast the cinnamon stick, cloves, peppercorns, and oregano for about 30 seconds until aromatic.
Toast the bread and tortillas until golden brown. Briefly fry the raisins until they plump.
Drain the soaked chiles and place them in a blender along with the tomatoes, onion, garlic, almonds, sesame seeds, peanuts (if using), bread, tortillas, raisins, spices, and 2 cups of stock. Blend until completely smooth.
Strain the sauce through a fine-mesh sieve into a large Dutch oven or heavy pot. For an especially silky texture, strain it a second time.
Heat the remaining 2 tablespoons of lard in the pot. Carefully add the strained sauce and cook for 5–10 minutes, stirring constantly.
Add the Mexican chocolate, salt, and 2 more cups of stock. Stir until the chocolate melts completely.
Bring the sauce to a gentle simmer and cook for 60–90 minutes, stirring frequently. Add additional stock as needed to keep the mole thick but pourable.
Add the cooked chicken or turkey and simmer for 10–15 minutes until heated through and coated in the sauce.
Serve topped with the reserved toasted sesame seeds.