In a large pot add pork, water, onion, garlic halves (minus the two reserved garlic cloves) and oregano. Bring to a boil, turn down to a simmer and cook until tender, one and a half to two hours.

In a dry skillet, lightly toast chile over a hot flame, turning often, until plump. Place in a small bowl and add enough water to cover. Weigh down with a plate or jar and soak for 30 minutes, longer is fine.

Remove chiles from water, reserving the soaking liquid. Remove stems and seeds. Place the chile in a blender with the reserved liquid. Peel the two cloves of garlic and add to blender. Do not process yet.

When meat is tender, remove the meat, onion, and garlic from the broth. When cool enough to handle, shred meat, discarding bones. Remove the cloves from the onion, add onion to blender. Discard the garlic halves or save to use in a salsa, dip or spread on toasted bread. Puree the chile mixture (with the onion and two cloves of garlic) and the reserved soaking liquid until smooth, adding a little broth if needed. Push the mixture through a sieve.

Skim the broth of excess fat. Add the shredded meat to the broth. Add the puree to the broth. Depending on personal taste, you may not with to add the full amount. Taste as you go. If you don’t use all the puree, pass at the table for those who wish to add more “oomph” to their pozole.

Rinse hominy well and add to the pot. Bring to a boil, turn down and simmer, very gently, for thirty minutes. Taste for seasoning and add salt if desired.

Garnish with thinly sliced radishes, thinly sliced onion that has been soaked in water for 30 minutes and thinly sliced cabbage. Add avocado, lime, and cilantro to the garnishes, if desired.

Pozole will generally keep four to five days in the refrigerator and freezes very well.