• Strain soaked hominy and rinse. Place in a large pot, add water to cover by at least 4 to 5 inches, and add the halved head of garlic. Set over high heat and bring to a rolling boil. Reduce to medium heat, skim off foam, cover partially and simmer for 2 1/2 to 3 hours, until the hominy “blooms” or opens up. Once the kernels are very soft and you see them opening on the top like a flower, add salt, stir, turn off the heat, and set aside and let cool. Do not continue to cook or the hominy will fall apart. If making the frijoles de olla, you may do so while the hominy cooks. If using canned hominy and beans, you may skip this step.

To cook the chicken:

• Do this while the hominy and beans are cooking. Place the cut up chicken in a large soup pot or casserole. Cover generously with water by at least 2 to 3 inches. Bring to a boil over high heat, reduce heat to medium-low, skim off foam and add the halved onion, 4 peeled garlic cloves, the quartered fresh Anaheim chile, 10 stems of cilantro and 2 teaspoons salt. Cover partially and simmer for 1 hour, until the chicken is falling away from the bone. Remove from heat, transfer the chicken pieces to a bowl and let cool until you can handle them. Strain the broth, set aside 1 cup, and return the rest to the soup pot.
• Discard the onion, garlic, Anaheim and cilantro. Remove the skin from the chicken and discard. Remove meat from the bones, tear it into small pieces, and return it to the strained broth.

To make seasoning sauce:

• Preheat the broiler with the rack adjusted at the highest setting. Cover a baking sheet with foil and top with the fresh Anaheim chile, the onion quarter, and the 2 unpeeled garlic cloves. Broil for about 10 to 12 minutes, flipping the vegetables over halfway through, until completely charred on the outside and soft on the inside. The garlic will be done before the other ingredients, usually halfway through, and should be removed from the baking sheet when you see that it is charred and softened. Alternatively, you can roast the vegetables on a comal over medium heat, flipping them over every 4 to 5 minutes, until charred.
• Place the chile in a plastic bag and let it sweat for 5 to 10 minutes. Remove the skin, stem and seeds from the chile and peel the garlic. Cut the chile into pieces and place it in a blender along with the charred onion, the peeled roasted garlic cloves and 10 sprigs of fresh cilantro. Add the cup of strained chicken broth that you set aside, and puree until completely smooth. Pour back into the soup pot or casserole with the chicken and remaining broth.
• Remove the onion from the pinto beans and stir the beans into the soup pot, along with 1 cup of their broth (or more, to taste). If using canned beans, rinse and add to the soup pot. Discard the halved head of garlic you added to the hominy and add the cooked hominy along with 1 cup of its liquid (or more to taste) to the soup pot. If using canned hominy, drain, rinse, and add to the pot.
• Return the pot to medium heat, bring to a simmer and simmer, partially covered, for 15 to 20 minutes. You will know it’s ready when the seasoning sauce pools on the surface into tiny dark green puddles that are a darker green than the rest of the soup. Taste and adjust salt.
• Serve and let everyone garnish with chopped white onion, cilantro, chiltepin chiles and a squeeze of fresh lime.