In a pan, over medium heat, cook onion and garlic in olive oil until tender and translucent. do not brown. Add cooked pork/chicken and adobo sauce, cook about 3-4 minutes, stirring occasionally. Add broth, hominy and seasonings, stir to combine. Bring to a boil, then reduce heat and simmer uncovered for about 30 minutes, stirring as needed.
Ladle soup into bowls. Top with cabbage, cilantro, cheese and tortilla strips. Squeeze with fresh lime wedge.