Season the chicken with salt and place it in a large pot with chicken broth. Bring to a boil, then reduce heat and simmer until fully cooked (about 20–25 minutes). Remove and shred the chicken, then return it to the pot.
In a blender, combine tomatillos, poblano pepper, jalapeños, onion, garlic, and cilantro. Blend until smooth.
Heat olive oil in a skillet over medium heat. Pour in the blended mixture, add cumin and coriander, and simmer for 5–6 minutes until slightly thickened.
Add the tomatillo mixture and hominy to the pot with the chicken. Simmer uncovered for 15–20 minutes. Season with salt and pepper.
Serve hot with your favorite toppings like cabbage, radishes, avocado, lime, and cilantro.