For the Menudo-style Fried Beef Tripe:
Using a wire brush, scrub the tripe. Blanch in boiling water, then scrub again, and repeat until clean. Once clean, cut into square 1-inch pieces.
Place the tripe, onion, garlic, chipotles, anchos, poblanos, oregano, salt, and pepper in a pot and cover with chicken stock. Bring to a simmer and cook until the tripe is tender (3 to 4 hours) and the liquid is reduced. Chill overnight. The following day, remove the tripe from the liquid and strain. Reduce the liquid into a sauce and season with soy sauce.
For the Duck Fat Beans:
Strain beans and combine with onion, garlic, and bay leaf, and cover with water. Bring to a simmer and cook until beans are tender. Salt, then strain beans, removing onion and bay leaf and reserving some liquid. Combine the beans, duck fat, hominy, onion and garlic powders in a blender with enough reserved liquid to create a thick purée; season with soy sauce and salt to taste.
For the Poached Egg:
Cook eggs in a water bath at 75°C for 13 minutes.
To Assemble and Serve:
Fry tripe until crisp in 375°F oil. Warm Duck Fat Bean purée and Tripe sauce.
Spoon Duck Fat Bean purée on plate, un-shell Poached Egg onto purée, top with Menudo-style Fried Beef Tripe, and spoon sauce over top. Garnish with onion and cilantro.