Prepare the chilies: Start by removing the stems and seeds from the dried chilies (ancho, pasilla, and mulato). Heat a skillet over medium heat and toast the chilies lightly for about 1-2 minutes, making sure they don’t burn. Once toasted, transfer them to a bowl and cover with hot water. Let the chilies soak for 15-20 minutes to soften.
- Toast the nuts and seeds: While the chilies are soaking, toast the sesame seeds, almonds, and peanuts in the same skillet over medium heat. Stir frequently for about 3-4 minutes until they are golden and fragrant. Set them aside.
- Make the mole sauce: In a large pot, heat the vegetable oil over medium heat. Add the chopped onion and garlic, sautéing until softened and fragrant, about 5 minutes. Add the tomatoes and cook for an additional 2-3 minutes until the tomatoes break down. Drain the soaked chilies and add them to the pot with the onion and garlic. Stir in the raisins, cinnamon, cumin, cloves, black pepper, cocoa powder, and sugar. Let everything cook for another 2-3 minutes.
- Add the toasted nuts, seeds, chocolate, and chicken broth to the pot. Stir to combine everything, and bring the mixture to a simmer. Let it cook for about 15-20 minutes to allow the flavors to meld together. Use an immersion blender (or a regular blender in batches) to blend the mole sauce until smooth and velvety. Taste and adjust the seasoning with salt and sugar as needed.
- Cook the chicken: While the mole sauce is simmering, season the chicken with salt and pepper. In a large skillet, heat the vegetable oil over medium-high heat. Add the chicken pieces and brown them on all sides until golden, about 5-7 minutes per side. Once browned, lower the heat to medium and cook for another 10-12 minutes, or until the chicken is fully cooked and the internal temperature reaches 165°F (74°C). Remove the chicken from the skillet and set aside.
- Combine the chicken and mole sauce: Once the mole sauce is smooth and rich, pour it over the cooked chicken in the skillet. Let the chicken simmer in the mole for about 10-15 minutes, allowing the flavors to blend together and the chicken to absorb the sauce.
- Serve: Serve the Mole Poblano hot, with the chicken pieces drenched in the rich mole sauce. Traditionally, this dish is served with rice, tortillas, or fried plantains, which soak up the delicious sauce. Garnish with sesame seeds and a side of lime wedges for added freshness.