Heat water in a big pot or dutch oven. Add pork meat, spare ribs, onion, and garlic, and cook over medium-high heat.
Bring to a boil, then reduce the heat to low and let simmer, partially covered, for about 2 ½ hours, or until the meat is almost done cooking. While cooking, skim the top layer of foam and fat from the pot using a ladle.
Season with salt when the meat is almost done.
Remove the pork from the broth. Trim excess fat, and remove meat from bones. Also, remove and discard the garlic and onion from the broth.
Strain the broth and return it to the pot. Shred the pork with two forks and return it to the pot.
While the pork is cooking, soak the ancho chiles and the guajillo chiles in just enough water to cover them, and let them soak for 25 to 30 minutes until they are soft.
Now add the soaked peppers, garlic, onion, and oregano into a blender along with about 1 cup of the cooking broth or water. Blend until smooth.
Heat oil in a large skillet over medium-high heat. Add the dry red chiles puree and salt to taste. Reduce the heat to medium and simmer, constantly stirring for about 25 minutes.
Using a strainer, add the sauce to the broth. Increase the heat to medium-high, bring to a boil.
After boiling, reduce the heat, cover, and gently simmer for about 10 minutes. Stir in the white hominy, and season with salt and pepper.
Serve Pozole in large Mexican soup bowls and place garnishes on the side.
