Prepare the chiles.

Stem and seed the roasted chiles, and cut the chiles into thin strips.

Reserve.

Put the chicken breasts in a saucepan.

Add the broth and bring to a boil, uncovered, then reduce the heat to low, cover and simmer until the meat is tender, 15 to 18 minutes.

Cool the chicken in the broth 15 minutes.

Remove the chicken from the broth, then remove and discard the skin.

Coarsely shred the meat, cover and reserve.

Strain the broth, cover, and refrigerate the broth for another use.

In a skillet, heat the oil over medium heat and cook the onion, stirring, 3 minutes.

Add the reserved chile strips, oregano, cumin, salt, and pepper.

Cook, stirring, 1 minute.

Reduce the heat to low and gently stir in the reserved chicken and crema.

Heat through completely, but do not boil.

Mound the chicken mixture on a serving platter and sprinkle the cheese on top.

Prepare the cilantro-mint sauce.

Cover and refrigerate.

Melt the butter in a large nonstick skillet, over medium heat, until it foams.

Cook the onion, stirring, until softened, about 3 minutes.

Add the corn and cook until tender, about 5 minutes.

Season with ¼ teaspoon of the salt and cumin.

Set aside off heat.

In another large skillet, heat the oil over medium heat until it shimmers and cook the chicken 4 to 5 minutes per side, or until browned on the outside, firm to the touch, and no longer pink inside in the thickest part.

To serve, place 1 chicken breast in the center of each of 4 plates.

Top each breast with some of the sauce.

Spoon the corn equally around the chicken on each plate.

Pass the remaining sauce at the table.

In a large saucepan, put the chicken, carrot, onion, half of the garlic, celery, parsley, bay leaf, and ½ teaspoon of the salt.

Add water to cover and bring to a boil.

Reduce the heat to medium-low, partially cover, and simmer 20 minutes.

Reserve off heat in the broth.

Meanwhile, in a medium dry skillet, over medium heat, lightly toast the almonds, stirring constantly, until fragrant and just beginning to brown, about 2 minutes.

Transfer to a blender or food processor.

In the same skillet toast the sesame seeds in the same way.

Add to the blender with the almonds.

Add the remaining garlic, allspice, clove, mint, and fresh jalapeño.

Pour in 1 cup of the reserved chicken broth.

Blend to a smooth purée.

Heat the oil in a large saucepan over medium heat.

Slowly add the sauce (so it doesn’t splatter), cover and cook, stirring frequently, about 8 minutes to blend flavors.

The sauce will thicken as it cooks, so stir in about 2 more cups (strained) chicken broth, a little at a time, to reach a consistency that coats the back of a wooden spoon.

Stir in the olives, capers, and pickled jalapeños.

Meanwhile, de-bone the chicken breasts and stir chicken pieces into the sauce.

Prepare the almond sauce.

Then, preheat the oven to 200°.

Put the sauce in an ovenproof bowl.

Cover and keep warm in the oven.

Trim the chicken of any visible fat.

Place each breast between 2 sheets of plastic wrap and pound it with the flat side of a meat mallet or with a rolling pin to an even 1⁄4-inch thickness.

In a large skillet, heat the oil over medium heat.

Season the chicken with salt and cook about 3 to 4 minutes per side or until lightly browned on the outside and no longer pink in the thickest part.

Serve hot with some of the sauce spooned over each breast.

Sprinkle with cilantro.

Pass the rest of the sauce at the table.

Prepare the chiles.

Then, remove the stems and seeds.

Cut one of the roasted chiles into short thin strips and reserve.

Chop the remaining 2 chiles and put them in a blender.

In a medium saucepan, heat 1 tablespoon of the oil over medium-low heat and cook the onion and garlic, covered, until the onion is translucent, about 4 minutes.

Transfer to the blender with the chiles.

Add the chicken broth and blend until smooth.

Return the blended mixture to the same saucepan.

Stir in the cream and ¼ teaspoon of the salt.

Bring to a boil, then reduce the heat and simmer, stirring, 4 to 5 minutes to blend the flavors.

Adjust seasoning and reserve off heat.

In a large nonstick skillet, heat the remaining tablespoon of oil and cook the chicken breasts 4 to 5 minutes per side, or until lightly browned on the outside, firm to the touch, and no longer pink inside at the thickest part.

Season with the remaining ¼ teaspoon of salt.

Reheat the sauce.

Serve with the heated sauce spooned over the chicken.

Scatter the reserved chile strips on top.

Prepare the chile sauce.

Then, heat the oil in a large nonstick skillet and cook the chicken about 4 minutes per side or until it is browned on the outside, firm to the touch, and no longer pink inside at the thickest part.

Season with salt.

Serve each chicken breast with a little of chile sauce spooned on top.

Sprinkle each serving with the sesame seeds.

Wipe the chiles with a damp paper towel.

Cut the chiles open, and remove the stems and seeds.

Heat a skillet over medium heat, and toast the chiles, turning, until they are aromatic.

(Do not burn or chiles will be bitter.

) Put the chiles in a bowl of hot water and soak to soften, about 20 minutes.

In a heavy medium saucepan, heat 2 tablespoons of the oil over medium heat.

Add the onion, garlic, and oregano.

Cook, stirring, until beginning to brown, 2 to 3 minutes.

Stir in the broth and orange juice.

Add the tomato paste, vinegar, sugar, and ½ teaspoon of the salt.

Bring to a boil, then reduce the heat to low, and simmer, stirring frequently, 5 minutes.

Put the saucepan contents into a blender or food processor.

Lift and drain the chiles from the soaking liquid, and add to the blender.

Purée until smooth.

(The sauce should be about as thick as ketchup.

) Return the sauce to the saucepan, and bring to a boil, then reduce heat to low, and cook, stirring frequently, about 8 minutes, to blend the flavors.

Remove the sauce from the heat, cover and reserve.

(Sauce can be made ahead to this point.

Refrigerate to store.

Reheat before serving.

)

Make a hot fire in an outdoor grill, or preheat a stovetop grill pan.

Brush the chicken breasts with the remaining oil, and season with the remaining ½ teaspoon of salt.

Cook the chicken about 4 to 5 minutes per side, or until lightly browned on the outside, firm to the touch, and no longer pink inside at the thickest part.

To serve, reheat the sauce and spoon a pool of sauce on each serving plate and place a chicken breast on each plate, or.

Cut each chicken breast crosswise into 1⁄2-inch strips and fan out over the sauce.

Garnish with cilantro.

Prepare the chipotle sauce.

Reserve.

Then mix together half of the olive oil, with the lime juice, garlic, and salt.

Coat the chicken pieces with the mixture.

Heat the remaining oil in a medium skillet and cook the chicken about 4 to 5 minutes per side or until golden brown on the outside, firm to the touch, and no longer pink inside at the thickest part.

To serve, spoon some of the chipotle sauce over each chicken breast.