To make the soup:
Rinse the tripe and calves’ feet, if using, in several changes of cold water.
In a bowl large enough to hold the tripe and calves’ feet, combine the vinegar, 4 cups of water, and 1 tablespoon of salt, stir to dissolve the salt. Add the tripe, calves’ feet, and enough additional water to cover and soak for 30 minutes. Drain in a colander and rinse well.
Cut the tripe into bite-size pieces, 1 to 1 1/2 inches.
Add 5 quarts of water and the onion and garlic in a very large soup pot or a stockpot. If using the calves’ feet, add them to the pot and bring the water to a boil over high heat. Reduce the heat to medium and simmer, partially covered, for 20 minutes. Skim off any foam.
Add the tripe to the pot, along with the remaining 1 teaspoon salt, the oregano, and mint-sprig bundle, and bring to a boil. Reduce the heat to low and simmer, partially covered, for 4 hours, or until the tripe is soft and tender but still has some texture. Remove the garlic and onion and discard.
Meanwhile, make the chile puree:
Place the dried chiles and garlic in a small saucepan, cover with water, and bring to a boil. Reduce the heat to medium-low and simmer for 10 to 15 minutes, until the chiles are softened. Remove from the heat and transfer the chiles and garlic to a blender, along with 1/2 cup of the cooking water. Add the cumin and coriander seeds and puree until smooth. Set aside.
To finish the soup:
If you used them, remove the calves’ feet from the pot with a slotted spoon and set aside to cool until you can handle them. Then remove the meaty and gelatinous pieces and discard the bones. Cut the meat and gelatinous bits into smaller pieces and stir back into the pot.
Bring back to a simmer. Add the chile puree, stir well to combine, and simmer for another 20 to 30 minutes to blend the flavors. Taste and adjust the salt.
Arrange the garnishes in small bowls on the table, and set out the tortillas, tostadas, or bread. Serve and let your guests customize their menudo.
Credit Pati Jinich