In a large Dutch oven, place pork roast and water. Bring to a boil. Add onions and salt. Reduce heat, cover, and simmer gently for 30 minutes. Add chicken and bring to a boil; reduce heat, cover, and simmer for 45 minutes. Remove pork and chicken from broth and allow to cool. Cover and refrigerate broth. Cut pork and chicken meat into small pieces and discard bones.
In skillet, heat bacon grease; add garlic, chili powder, and paprika; stir just until blended. Add small amount of broth and stir. Add mixture and hominy to broth and bring to a boil. Reduce heat, cover, and simmer gently for 30 minutes; add pork and chicken pieces and simmer until meat is thoroughly heated, about 15 minutes. Serve in individual bowls with garnishes as side dishes.
Fun Fact: The ancient village of Oraibi, located on the Third Mesa of the Hopi Indian Reservation in Arizona, is the oldest continuously inhabited community in the country; the community began around 1100 AD. Ácoma Pueblo, New Mexico, also called Sky City because it sits atop a 357-foot mesa, was founded about the same time. Mesas are the flat-topped mountains found in the desert.
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