Cut the honeycomb tripe into medium-sized squares and transfer it to a large container, preferably one with a strainer insert.
Cover the tripe with water, rubbing gently to clean, then drain and rinse. Repeat this process twice. Refill the container with water, stir in the juice of five limes, and leave the lime skins in the water.
Add the cow’s feet and let them sit in the lime water with the tripe for 30 minutes. Then remove the lime skins, rinse everything two more times—or until the water runs clear—and drain all the water.
Start the Menudo
Place the cow’s feet, onion, garlic, bay leaves, epazote, and water in a large pot. Bring to a boil over medium-high heat, then reduce to medium-low. Cover, skim off any foam or scum, and let it simmer gently for 30 minutes.
After 30 minutes, add the cleaned honeycomb tripe to the pot. Bring the mixture back to a boil over medium-high heat, then reduce to medium-low and continue simmering for 2 hours.
Toast Chiles
Clean the chiles de árbol with a damp paper towel and let them air dry. Toast them on a comal over low heat, turning continuously until fragrant, then set aside to use as a topping.
Toast the guajillo and puya chiles in the same way, then place them in a heat proof container, rinse, drain, and cut into pieces that fit comfortably inside. Cover with hot water and rehydrate for 5–10 minutes, or until soft and pliable.
Make the Chile Sauce
In a blender, combine the hydrated guajillo and puya chiles, 3 cups of the chile soaking liquid, garlic, cumin, and oregano. Blend until smooth. Strain if necessary.
Finish Menudo
After 2 hours of simmering the tripe, remove the onion, garlic, and epazote from the broth. Stir in the sauce, then pour an additional cup of chile soaking liquid or water into the blender to get any remaining sauce and add it to the pot. Optionally, skim off extra fat from the surface.
Bring the soup back to a boil over medium-high heat, then reduce to medium-low. Cover and simmer gently for another 30 minutes. At this point, the tripe and cow’s feet should be tender.
Add salt to taste. Remove the cow’s feet and any loose bones from the pot. Separate the tissue, tendons, and skin from the bones, cut into bite-sized pieces, and return to the pot. Discard the bones.
Serve
After stirring the pot to combine everything, serve the menudo in bowls. Top with chopped cilantro, diced onion, toasted chiles de arbol (broken into small pieces), oregano, lime juice, and avocado. Enjoy with corn tortillas.