In a 4-liter pot, heat the chicken stock. Add the pieces of chicken, then cover the pot, lower the heat, and cook until the chicken is soft, about ½ hour. Add salt to taste.
Remove the pieces of chicken from the broth, then cook the potatoes, green beans, squash and chayotes in the broth, each one separately, until they are soft. Set these aside and reserve the broth.
Boil 2 cups of water. Using a dry comal, griddle or frying pan, char the skin of the peppers over medium heat until they begin to form blisters and start to release their aroma. Remove the peppers from the comal and place them in a bowl to soak for 20 minutes in the hot water. Afterwards, drain the peppers and reserve the water.
Put the peppers in your blender along with 1½ cup of the soaking water and grind until you obtain a smooth puree. Pass the puree through a strainer; this will prevent the little pieces of pepper skins from getting in the sauce. Set aside in a bowl.
Lightly toast cloves, allspice, peppercorns and oregano on the griddle/comal until they release their aroma. Remove promptly and add to your blender.
In a 2-liter saucepan, boil the tomatoes and miltomates (or tomatillos) in 1 cup of water until the miltomates begin to change color, about 10 minutes. Peel the tomatoes and discard their skin.
Add the tomatoes, miltomates, onion, garlic, and 1 cup of the reserved chicken broth to your blender, and blend until you obtain a smooth puree. Pass this puree through a strainer to remove the seeds.
In a 4-liter pot, heat the lard or oil until it is very hot. Then, fry the pepper puree over medium heat for about 15 minutes, stirring frequently. Add the puree of tomatoes and spices and fry them together for another 15 minutes.
Put the corn masa and 1 cup of the broth in your blender and grind well. Add this to the tomato and pepper mixture in the pot. Let thicken for about 15 minutes, stirring frequently. Add a tablespoon of salt or more, to taste.
Dilute the mole sauce with 2 or 2 ½ cups of broth, or more, if needed. It should be thick enough to cover the back of a spoon.
Add the leaves of Hierba Santa to the mole. Keep warm.