Turn a pressure cooker to Saute High, once the pot is hot, add the olive oil. Cook the diced onion until soft, and then add the garlic, cumin, oregano, and jalapeno (if you're using one). Stir for one minute.

Add a little chicken broth to the bottom of the pot to scrape up the bits on the bottom of the pot. Press the Cancel button on the pot to stop the pot from cooking the ingredients. Turn the pot to Manual (some models call this Pressure Cook).

Add the chicken broth, hominy, tomatoes, lime juice, and chicken pieces.

Pressure cook the soup ingredients for 10 minutes and then do a natural release for 5 minutes. When the pin drops, open the pot, give the soup a stir and add salt and pepper to taste.

Ladle the pozole into soup bowls and then add the shredded cabbage, radishes, cheese, and green onion. Other garnishes you can add include sour cream, tortilla chips, or guacamole.

Bring water to a boil in a Dutch oven or large soup pot. Add the chicken, cover the pot with a lid, and simmer the chicken until it's cooked through. This will take about 12-13 minutes.

Remove the chicken from the broth and set it aside. 

Add the hominy, tomatoes, oregano, cumin, jalapeno, lime juice, and a dash of hot pepper sauce to the chicken broth in the pot.

Bring it to a boil, reduce the heat, and simmer the soup mixture stirring often until it's slightly thickened. 

In the meantime, after the chicken cools, shred it.

Stir the shredded chicken into the pot, along with the fresh cilantro, and additional salt and pepper, if desired. Heat until the chicken is warm again.

Ladle the chicken pozole into soup bowls and then add the shredded cabbage, radishes, cheese, and green onion. Other garnishes you can add include sour cream, tortilla chips, or guacamole.