In a large heatproof bowl, combine the guajillo and ancho chiles. Add 10 cups of boiling water and set aside until the chiles are soft, about 15 minutes; drain, reserving the soaking water.
Pat the meat dry with paper towels, then sprinkle it all over with the kosher salt. Set aside for 10 minutes.
Meanwhile, transfer half of the chiles and 8 cups of the reserved soaking liquid to a blender. Add half the onion and 3 garlic cloves and blend until smooth. Set a fine-meshed sieve over a deep, heavy cast iron pot or Dutch oven and strain the mixture into the pot, stirring as needed to help it through.
To the blender, add the remaining chiles, soaking liquid, onion, and garlic, as well as the cloves, peppercorns, and bay leaves. Blend until very smooth. Set the sieve over a medium bowl, strain the purée through, and set aside.
Add half of the avocado leaves and use a spoon to arrange them along the bottom of the pot. Place the meat in the pot, then layer the remaining avocado leaves on top of the meat. Pour the reserved chile purée over the leaves, set the pot over medium heat and bring to a simmer. Lower the heat to low heat to maintain a simmer, and let cook until the meat is very tender, 4–5 hours.
Meanwhile, prepare the broth. In a medium pot, combine the potatoes with 6 cups salted water. Bring to a boil over medium-high heat, then lower the heat to maintain a simmer. Cook until the potatoes are firm-tender, 10–11 minutes. Add the chickpeas and green beans and continue cooking until the green beans are bright green and firm-tender, 5–6 minutes more. Remove from heat and set aside.
When the meat is done, remove from heat. Use two large spoons to transfer the meat into a large bowl. Remove and discard the leaves but leave the braising liquid in the pot. Transfer the cooked vegetables and their cooking liquid to the large pot of meat braising liquid. Finely chop the remaining onion half, the hoja santa, and the cilantro, and add them to the pot as well. Bring to a simmer over medium heat and cook until the onions are soft and the liquid is reduced slightly, 25–30 minutes.
To serve, coarsely shred the meat and divide it between 6 deep bowls. Fill each bowl with broth and some of the vegetables. Serve with additional cilantro, lime wedges, and corn tortillas.