Heat olive oil in a large pot over medium heat.
Add chopped onion and cook until translucent, about 5 minutes.
Add minced garlic, diced carrots, and diced celery. Cook for another 5 minutes.
Stir in hominy, vegetable broth, ground cumin, dried oregano, and chili powder. Bring to a boil.
Reduce heat and simmer for 20 minutes.
Add shredded vegan chicken and cook for another 10 minutes.
Season with salt and pepper to taste.
Serve hot, garnished with shredded cabbage, sliced radishes, chopped cilantro, and lime wedges.