Heat a large skillet over medium-high heat (no oil). You're going to roast (or toast) the first 7 ingredients in this skillet.
First add all the chile peppers and roast 2-3 minutes, turning once. Remove from skillet and place on cutting board. Cut peppers in half lengthwise and remove seeds. Place in a bowl and pour enough boiling water over the peppers to cover. Let them soak for about 10 minutes.
While peppers are soaking, toast the peppercorns, cloves and cumin seeds for 1-2 minutes or until just fragrant. Remove from skillet and grind up in a spice grinder until finely ground.
Roast the tomatillos, tomato and onion about 7 minutes or until charred, turning occasionally. Add the garlic for the last minute or so. Remove everything from heat until cool and then peel them. *note: you can put the tomatillos and tomato in a paper bag and close it up for a bit to make them easier to peel.
Drain the chile peppers and add the peppers, peeled tomatillos, tomato and onion to a food processor and process until smooth. Add the spices and process until combined.
In a medium saucepan, heat the oil over medium-high and add the processed pepper mixture and salt and bring to a boil. Reduce heat and simmer about 10 minutes.
In a small bowl whisk together the water and corn meal and add to the simmering pepper mixture. Cook briefly until it reaches a low boil.
In a 6-quart Dutch oven, bring the 4 cups chicken broth to a boil. Add the chicken thighs and reduce the heat. Cover the pot and simmer about 15 minutes. Then add the chayote and asparagus. Simmer, covered 10-15 more minutes until chayote is tender.
To serve: Transfer the chicken thighs and vegetables to a plate with a slotted spoon (unless you want more of a soup) and spoon the mole over the chicken and vegetables. Garnish with cilantro if desired.