Step 1Soak the garbanzo beans with at least 2 quarts of water overnight to soften. Drain, rinse and drain again. Set aside.
Step 2Heat a thin film of oil in a large, heavy pot over medium heat. Add the onion and chiles and cook, stirring frequently, until softened and translucent, 6 to 8 minutes. Add the garlic and cook until aromatic, about 1 minute. Stir in the mushrooms and tomatillos. Cook, stirring occasionally, until the mushrooms and tomatillos have softened and released most of their juice, about 8 to 10 minutes.
Step 3Stir in the drained garbanzo beans, along with the vegetable broth. Increase the heat so the soup base slowly comes to a boil.
Step 4While the soup is coming to a boil, toast the tortillas. Heat a skillet or comal over high heat until hot. Briefly toast each tortilla on each side until fragrant and lightly colored. Set aside.
Step 5Add the toasted tortillas, corn, oregano and cumin to the soup base and reduce the heat to a gentle simmer. Cook the soup, stirring occasionally, until the garbanzos are tender, the tortillas have broken down, and the liquid is reduced so the soup is the desired thickness (if the soup is too thick, add additional broth or water to thin as desired), stirring occasionally, about 1 hour. Stir in the lime juice and salt. Taste the soup and adjust the flavoring and seasoning if desired.
Step 6Ladle the hot pozole into bowls and garnish with cabbage, onion, lime wedges and cilantro. Serve immediately.