Place chicken, chayote, broth and salt in a large pot and bring slowly to a boil, reduce heat and let simmer until the chicken is cooked through..

While the chicken is simmering, put tomatoes, tomatillos, onions and garlic on a cast-iron or nonstick skillet. Turn the heat on to medium and let the vegetables dry-roast. Turn them with tongs and let them get charred on all sides. The onion peels might start to look pretty black, but you’ll remove the outer skins anyway. This will take 15 minutes or so. When they are soft and roasted, move them on a plate where they can cool enough to handle.

While the vegetables are roasting, and in another dry skillet, put the sesame seeds, pepitas, cinnamon, and red pepper flakes over low heat. Toast them, tossing, and once you can smell and see they are toasted, remove them from the heat and pour into blender. Set the pan back on the heat and now toast the pasilla, guajillo and ancho chiles, lightly, turning them a few times. When you can smell the chiles becoming fragrant take them off heat and set asisde. Now, put the corn tortillas into the pan and again, let them toast, dry, until they are crisped.

Blend the toasted seeds and spices in the blender to a coarse powder. Take the stems off and seeds out of the dried, toasted chilies and put them into the blender along with the crisped tortilla. Blend this mixture well, add a cup or so of chicken broth to help the process along. Turn this finely blended mixture into a bowl and set aside.

Next, trim stem ends and skins from the cooled, pan-roasted vegetables. The softened garlic will come right out of the skins. Put these into the blender along with the cooked chayote and blend to a smooth sauce. Add the tomatoes and onion mixture to the the seeds and chiles mixture and mix well. Add the achiote and pepper and whirl until smooth. Add salt to taste

Now, drain the chicken stock from the pot with the cooked chicken and set aside. Then, pour in the contents of the blender, stir gently and add 2 cups of the chicken broth. Simmer the chicken until fork tender (another 15-20 minutes) in the mixture. If it gets too thick, add some more broth. It should be a smooth, thick sauce that coats the chicken pieces well.

Serve pieces of chicken on a plate covered generously with the sauce, garnished with sesame seeds. Serve with white rice and more warm, corn tortillas.