Step 1: Peel onion, cut in half and set aside. Strip the thyme leaves from the stems, you'll need a teaspoon. Reserve the stripped stems for later use.
Step 2: First make the broth base in a blender jar. Add 1/2 the onion, the garlic cloves, just 2 bay leaves, the thyme leaves, the chicken bouillon, and the Mexican oregano. Add 4 cups of the water, the vinegar, and 1 cup of the drained hominy. Blend until smooth. Set aside.
Step 3: Pat the pork dry, then cut into 2-3 inch chunks. Salt generously and massage into pork.
Step 4: Melt the lard in a large Dutch oven or deep pot, at least 8 1/2 quarts. Working in batches, add the pork in a single layer. Brown each side, about 3 minutes per side. Remove pork and continue until all is browned. After the last batch, return all the pork to the pot.
Step 5: Pour in the broth base. Add 10 cups water. Add the remaining 1/2 onion, remaining 2 bay leaves, the stripped stems from the thyme. Bring to a boil, then reduce to a simmer. Cover and cook for 60-80 minutes, until the pork is cooked through and shreds easily.
Step 6: Remove the onion, bay leaves, and thyme stems. Add the rest of the hominy. Cover and bring back to a simmer. Cook for an additional 30 minutes.
Step 7: While the pozole finishes its final cooking time, prepare the toppings: thinly shred the cabbage, thinly slice the radishes, finely dice the onion. Prepare the chile de arbol salsa, if using, during this time. See my recipe #12496.
Step 8: To serve, ladle broth, pork and hominy into wide shallow bowls. Place the toppings into individual serving dishes at the table and allow everyone to add toppings to their taste, along with a squeeze of lime.
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