Trim off excess fat from the tripe and cut into bite-size pieces. Thoroughly rinse tripe, ox feet, and pig’s feet.
In a large (at least 10-quart) pot, over high heat, put 8 cups water and the ox feet, half the chopped garlic, the ½ onion, and 1 tablespoon of salt. Let it come to a boil uncovered. After it starts to boil, lower heat, cover, and simmer for 3 hours.
Add the pig’s feet to the ox feet pot and simmer for another 3 hours.
Meanwhile, in a separate large (at least 14-quart) pot, put the tripe, 10 cups water, remaining garlic, the quartered whole onion, and 1 tablespoon salt. Let it come to a boil uncovered. After it starts to boil, lower heat, cover, and simmer for 3½ hours. Tripe will produce extra liquid during the cooking. Remove 2 cups stock and reserve for later use, if necessary. (Never add water from faucet to the soup, you will dilute the taste. Use this reserved stock.)
After the ox and pig’s feet are cooked, add the feet and liquid to the pot with the tripe. Add the red chile sauce and the hominy and let it come to a boil. Lower heat to low, cover, and simmer for 1½ hours.
Stir in oregano. Skim any excess fat off the surface before serving. Place garnishes in separate bowls on the table.
Spoon portions of broth, meat, and hominy into soup bowls. Let your guests add the garnishes to suit their own taste. Serve with fresh or grilled bolillos (rolls).
If you have any leftovers, refrigerate and then remove any fat that jellied at the top before reheating.
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