Step 1

Place 16 cups water, 3 (29-ounce) cans rinsed and drained white hominy, 3 1/2 pounds boneless pork shoulder chunks, 1/2 trimmed and peeled medium white onion, 1 trimmed head garlic, 1 tablespoon of the dried oregano, and 1 tablespoon of the kosher salt in a large stockpot (at least 8 quarts). Bring to a boil over medium-high heat. Reduce the heat to maintain a simmer and cook until the pork is tender, about 1 hour. Meanwhile, prepare the guajillo chiles and make the salsa.

Step 2

Place 12 stemmed large dried guajillo chiles in a medium saucepan and add enough water to just cover the chiles. Bring to a boil over medium heat. Reduce the heat to maintain a simmer and cook until the chiles are softened and darkened in color, about 10 minutes. Transfer the chiles with tongs to a bowl; discard the cooking liquid.

Step 3

Cook 14 trimmed dried arbol chiles in a small frying pan over low heat, stirring often, until fragrant and starting to char in spots, 2 to 3 minutes. Transfer to a blender. Add 1 cup water, 1 peeled garlic clove, 1/2 teaspoon kosher salt, and 1/4 teaspoon distilled white vinegar. Blend until smooth.

Step 4

Pour through a fine-mesh strainer set over a small bowl and push it through with a flexible spatula; discard the contents of the strainer. Stir 1/2 cup finely diced cucumber into the salsa. Taste and season with kosher salt as needed. Rinse out the blender.

Step 5

Using a slotted spoon, transfer the onion and garlic head from the pozole to the bowl with the guajillos and let cool for 5 minutes. Meanwhile, transfer 1 cup of cooking pork liquid to the blender.

Step 6

Squeeze the garlic cloves out of the head. Add the garlic cloves and reserved onion, guajillos, remaining 1 1/2 teaspoons kosher salt, and 1 tablespoon plus 1 1/2 teaspoons chicken bouillon powder to the blender. Blend until smooth.

Step 7

Pour through a strainer set over a small bowl. Push it through with a flexible spatula; discard the contents of the strainer. Stir the strained mixture and remaining 1 tablespoon dried oregano into the pozole.

Step 8

Simmer uncovered until the flavors meld and broth deepens in color, about 30 minutes. Taste and season with more kosher salt as needed. Serve with the chile de arbol salsa (it’s very spicy, so start with stirring in just a little), tostadas, and desired toppings.