In a large pot or Dutch oven, heat the olive oil over medium-high heat. Add the onions, jalapeño, and poblano peppers, and sauté for 3-4 minutes until the onions start to turn translucent. Add garlic and tomatillos, stirring regularly, and cook for 4-5 minutes or until the peppers have softened. Remove from heat.
Transfer the onion mixture to a blender, and add about 1 cup of chicken broth. Add fresh cilantro and blend until smooth, adding additional broth if needed.
Return the blended mixture to the pot, and add the remaining chicken broth, dried oregano, ground cumin, ground coriander, bay leaf, and salt. Stir well to combine.
Place the chicken in the pot and bring the mixture to a boil over medium heat. Reduce heat to low, partially cover, and simmer for 30 minutes or until the chicken is tender and fully cooked.
Remove the chicken from the pot, shred it with two forks, and return it to the pot. Stir in the hominy.
Cook the soup uncovered for 10 minutes over medium heat. Taste and adjust seasoning with chicken bouillon, salt, and black pepper as needed. Let it simmer for an additional 5 minutes.
Serve the soup in bowls, garnished with your favorite toppings like sliced radishes, avocado, jalapeños, lime wedges, fresh cilantro, shredded cabbage, and tortilla chips.