Season chicken pieces generously with salt and pepper. Heat oil in a large Dutch oven over medium-high heat and brown chicken on all sides, about 8-10 minutes total. Remove and set aside.
In a dry skillet over medium heat, toast the dried chilies one type at a time until fragrant and slightly puffed, about 30-60 seconds per side. Don't let them burn.
Place toasted chilies in a bowl and cover with hot chicken broth. Let soak for 20 minutes until softened.
Meanwhile, toast almonds and sesame seeds in the dry skillet until golden and fragrant, about 3-4 minutes.
In a blender, combine the soaked chilies with their liquid, toasted nuts and seeds, onion, garlic, and all spices. Blend until completely smooth, working in batches if needed.
Strain the mole sauce through a fine-mesh sieve into the Dutch oven, pressing solids with a spoon to extract maximum flavor.
Bring sauce to a simmer over medium heat, stirring frequently. Cook for 15 minutes, then stir in chocolate until melted.
Return chicken to the pot, nestling pieces into the sauce. Cover and simmer for 25-30 minutes until chicken is cooked through and sauce has thickened.
Taste and adjust seasoning with salt. Serve immediately, garnished with sesame seeds and warm tortillas or rice.
Notes
Mole sauce can be made 3 days ahead and refrigerated. The sauce freezes well for up to 3 months. Thin with warm broth if needed when reheating.