Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the chopped onion, jalapeño, and poblano peppers. Cook, stirring often, for 3 to 4 minutes until the onion becomes translucent.

Stir in the minced garlic and quartered tomatillos. Continue cooking, stirring regularly, for 4 to 5 minutes until the peppers have softened. Remove the pot from heat.

Transfer the cooked vegetable mixture to a blender. Add about 1 cup of the chicken broth (cold is fine) and the fresh cilantro. Blend until completely smooth, adding a little more broth if needed to help it blend.

Pour the blended sauce back into the pot. Add the remaining chicken broth, dried oregano, ground cumin, ground coriander, bay leaf, and salt. Stir well to combine.

Add the chicken thighs (or breasts) to the pot. Bring the soup to a boil over medium heat, then reduce the heat to low. Cover the pot partially and let it simmer for about 30 minutes, or until the chicken is tender and cooked through.

Carefully transfer the cooked chicken to a plate or cutting board. Use two forks to shred the chicken into bite-sized pieces. Return the shredded chicken to the pot.

Stir in the drained and rinsed hominy. Cook uncovered over medium heat for 10 minutes. Taste the soup; if it lacks depth, stir in the chicken bouillon. Simmer for another 5 minutes, then season with salt and ground black pepper to taste.

Ladle the pozole verde into soup bowls and let everyone add their favorite toppings, such as sliced radishes, avocado, jalapeños, lime wedges, cilantro, shredded cabbage, or tortilla chips.