Prepare the Chiles:

1. Stem and Seed: Remove the stems and seeds from the dried ancho, pasilla, and mulato chiles.
2. Toast: Heat a dry skillet over medium heat. Toast the chiles lightly for about 30 seconds per side, just until fragrant. Be careful not to burn them. Transfer to a bowl and cover with hot water. Let soak for about 20 minutes until softened.

Make the Mole Sauce:

1. Blend the Chiles: Drain the chiles and place them in a blender or food processor. Add a small amount of the soaking liquid and blend until smooth. Set aside.
2. Cook Aromatics: Heat 1 tablespoon of vegetable oil in a large saucepan over medium heat. Add the chopped onion and cook until translucent, about 5 minutes.
3. Add Garlic: Stir in the minced garlic and cook for another minute.
4. Combine Ingredients: Add the blended chiles, diced tomatoes, peanut butter, sesame seeds, cocoa powder (or Mexican chocolate), raisins, cumin, cinnamon, and oregano to the saucepan. Stir well to combine.
5. Simmer: Gradually add the chicken broth while stirring to smooth out the mixture. Bring to a simmer and cook for about 20 minutes, stirring occasionally, until the sauce thickens and the flavors meld. Adjust seasoning with salt, and add sugar or vinegar if desired for balance.

Cook the Chicken:

1. Season: Season the chicken thighs and drumsticks with salt and pepper.
2. Brown the Chicken: Heat 1 tablespoon of vegetable oil in a large skillet over medium-high heat. Add the chicken pieces and cook until browned on all sides, about 5-7 minutes per side. The chicken does not need to be cooked through at this stage.

Combine Chicken with Mole Sauce:

1. Simmer Together: Place the browned chicken pieces in a large pot or Dutch oven. Pour the mole sauce over the chicken. Ensure the chicken is mostly covered with the sauce.
2. Cook: Bring to a simmer, cover, and cook for about 30-40 minutes, or until the chicken is cooked through and tender. The internal temperature of the chicken should reach 165°F (74°C).

Serve:

1. Plate the Dish: Serve the chicken with mole sauce over a bed of cooked rice. Accompany with warm tortillas on the side.
2. Garnish: Optionally, garnish with chopped fresh cilantro and lime wedges.