In a large pot or Dutch oven, heat the olive oil over medium heat. Add the chopped onion and sauté until soft and translucent, about 5 minutes.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the chicken thighs to the pot and pour in the chicken broth. Bring to a simmer.
While the chicken cooks, in a blender or food processor, combine the tomatillos, jalapeño, cilantro, cumin, and oregano. Blend until smooth and set aside.
After the chicken has simmered for about 30 minutes, remove it from the pot and shred it using two forks.
Return the shredded chicken to the pot, then add the hominy and the blended green sauce. Simmer for another 15 minutes to allow flavors to meld.
Season the pozole verde with salt and pepper to taste.
Serve hot in bowls, garnished with lime wedges, sliced radishes, shredded cabbage, and avocado slices as desired.