How to Make It
Heat oil in a large skillet over medium-high. Sprinkle chicken with 1 teaspoon of the salt, and add to skillet. Cook until browned, 3 to 4 minutes per side. Transfer chicken to a 5- to 6-quart slow cooker.
Add onion and garlic to drippings in skillet; cook, stirring occasionally, until softened, about 4 minutes. Add green chiles, cumin, and oregano; cook, stirring often, until fragrant, about 1 minute. Transfer to slow cooker; stir in chicken broth and remaining 1 teaspoon salt. Cover and cook on LOW until chicken is tender, 3 1/2 to 4 hours, adding hominy for the last 30 minutes. Remove chicken from slow cooker; shred and return to slow cooker. Add cheese, stirring until cheese melts. Garnish with radish slices, cilantro, and avocado. Serve with lime wedges and tortilla chips.