Bring skin and bones, chicken broth and 1 quart of water to boil over medium-high heat. Reduce heat to low and simmer about 30 minutes. Strain and discard skin and bones.
Heat oil over medium-low heat in a soup kettle. Add cumin, oregano and cayenne and cook until spices are fragrant, about 1 minute. Add onion; increase heat to medium; saute until soft, 4 to 5 minutes. Stir in chicken and chiles. Add 4 cups hominy and all but 1 cup of the broth and bring to a simmer. Reduce heat to low and simmer, uncovered, stirring occasionally, 25 to 30 minutes.
Process remaining 2 cups hominy and 1 cup broth until silky smooth; add to soup. Stir garlic and corn into soup. Simmer for a minute or so longer, then cover and let stand for 5 minutes.
Ladle into bowls and top with sour cream, cilantro or scallions. Pass separately the lime wedges and green hot pepper sauce.
2 store-bought roast chickens (meat picked from bones)
2 quarts chicken broth
6 tablespoons vegetable oil
1/4 cup ground cumin
4 teaspoons dried oregano
1/2 teaspoon cayenne pepper
2 large onions (cut into medium dice)
2 (4 ounce) jars diced mild green chiles
2 (20 ounce) cans hominy (or equal quantity of canned white beans such as cannellini)
6 medium garlic cloves (minced)
2 cups frozen corn, preferably shoepeg
cilantro or scallions
green hot sauce