In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and chopped jalapeño peppers, cooking for an additional 2 minutes until fragrant.
Add the tomatillos to the pot and cook for about 5 minutes, stirring occasionally, until they begin to soften.
Pour in the chicken broth and bring the mixture to a simmer. Add the shredded chicken, hominy, ground cumin, and dried oregano. Season with salt and pepper to taste.
Let the pozole simmer for 20-30 minutes, allowing the flavors to meld together.
Stir in the chopped cilantro just before serving.
Serve hot with lime wedges, sliced radishes, and diced avocado on the side for garnishing.