In a large pot or Dutch oven, heat the olive oil over medium heat. Once hot, add the chopped onion and sauté for about 5 minutes, or until translucent. Add the minced garlic and stir for an additional minute until fragrant.
Introduce the chopped poblano and jalapeño peppers to the pot. Cook for about 5-7 minutes, stirring occasionally, until they soften.
Add the chopped tomatillos to the pot along with the ground cumin, ground coriander, dried oregano, and salt. Stir well to combine all the ingredients, allowing the tomatillos to cook down for about 5 minutes.
Nestle the boneless chicken pieces into the mixture and add the bay leaf.
Carefully pour in the chicken broth, ensuring that the chicken is mostly submerged. Bring the mixture to a gentle boil.
Once boiling, reduce the heat to low, cover the pot, and let it simmer for about 40-45 minutes, or until the chicken is cooked through and tender.
After the chicken is cooked, remove it from the pot and shred it using two forks. Return the shredded chicken back to the pot and stir to combine.
Stir in the chopped cilantro for a burst of freshness. Taste and adjust the seasoning if necessary.
Ladle the Chicken Chili Verde into bowls and garnish with additional cilantro, sliced avocado, and lime wedges if desired.