In a large pot add 2 cups of water and the drained hominy
In a separate large pot, place the chicken pieces and add enough water to cover by a couple inches. Add the onion, cilantro, and 1 tablespoon of salt.
Bring to a boil then reduce heat to a simmer over medium low and cover.
Cook for about 45 minutes until the chicken is cooked and tender Remove the chicken pieces from the pot, strain and reserve the cooking liquid.
When the chicken is cool enough to handle, remove and discard the skin and bones and shred the meat.
Put the chicken and the reserved liquid into the pot with hominy. Place the pot over medium heat until warm. Add salt if needed
For the red sauce:
Place the chilies in a medium sauce pan, add just enough water to cover and bring to a boil. Reduce to simmer and until the chilies are soft, about 10 minutes or so.
Put the chilies and 3/4 cup of the soaking liquid into a blender along with the onion, garlic, cloves, cumin, and salt. Blend until smooth.
Run this through a fine mesh sieve into a bowl, using a spoon to extract as much liquid as possible. Discard what does not go through.
Heat the vegetable oil in a saucepan over medium high heat until it comes to a simmer, add in the chili liquid and bring to a boil then reduce to simmer, stirring occasionally. The sauce with thicken cook in total about 5 or 6 minutes and remove from heat.
Assuming your pozole is still warm turn up the temperature to medium high.
Stir in the chili mixture and add salt to taste.
Serve the pozole hot with the accompaniments listed above. Make sure to squeeze lime over the soup, it makes the dish complete.