Place the chicken thighs, zucchini, potatoes, carrots, chicken broth, and 1 teaspoon of salt into a large pot. Bring to a boil, reduce the heat, and simmer until the chicken is no longer pink and the vegetables are tender, about 20 minutes. Remove the chicken and vegetables from the pot, reserving the broth, and set aside.
Mix the masa harina with water in a small bowl, and let stand until the corn flour has absorbed the water and made a pliable dough, about 10 minutes. Form the masa dough into a 2 inch ball. Place the dough ball, tomatoes, tomatillos, garlic, onion, guajillo peppers, cinnamon stick, cumin seeds, cloves, peppercorns, epazote, and achiote seed into the broth, bring to a boil, reduce the heat, and simmer until the vegetables are tender, about 20 minutes.
Discard the cinnamon stick, and remove the vegetables and dough ball from the broth with a strainer. Place them into a blender, and working in batches if necessary, blend the ingredients until mostly smooth. Strain the sauce, and set it aside. Retain about 1/2 cup of broth.
Heat the olive oil in a large pot over medium heat, and slowly pour the sauce into the hot oil, letting it fry and bubble until it starts to change color, about 3 minutes. Add the chicken, zucchini, potatoes, and carrots to the sauce, pour in about 1/2 cup of reserved chicken broth, and stir. Season with salt to taste, and simmer over low heat for about 10 minutes to blend the flavors.