Trim stems from chiles; cut chiles lengthwise but not all the way through, and remove seeds. Transfer chiles to a small saucepan, and add 4 cups water. Bring to a boil over high; boil until softened, about 8 minutes. Set aside.

While chiles cook, heat avocado oil in a 6-quart pot or Dutch oven over medium-high. Add mushrooms, onion, and bay leaves, and cook, stirring often, until onion is translucent and mushrooms start releasing liquid, about 5 minutes. Reduce heat to medium, and cook, stirring often, 5 minutes. Remove from heat.

Drain chiles, reserving 2 cups soaking liquid. Place chiles, reserved soaking liquid, and garlic in a high-powered blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process chile mixture until smooth, about 45 seconds.

Pour chile mixture through a fine wire-mesh strainer directly into mushroom mixture in pot; discard strained solids. Add hominy, salt, and 6 cups broth; stir to combine. Bring to a boil over medium-high; reduce heat to medium. Cover pot, and boil pozole, undisturbed, 35 minutes. Season with additional salt to taste; add up to remaining 2 cups broth as needed if pozole is too thick. Cover and continue cooking pozole over medium, undisturbed, 10 minutes.

Remove pot from heat, and let pozole rest, covered, 10 minutes. Remove and discard bay leaves. Serve with cabbage, radishes, lime wedges, cilantro, and chips or tortillas.