Position an oven rack about 6 inches from the broiler and turn the broiler on high. Place the tomatillos, quartered onion, poblano peppers, and jalapeño on a baking sheet. Broil for 5-7 minutes, until the tops are blackened and blistered. Flip the vegetables and broil for another 4-5 minutes until charred on the other side.

Carefully transfer the charred vegetables to a blender. Add the garlic cloves, fresh cilantro, and 1/2 cup of chicken broth. Blend until smooth.

Place the chicken breasts in the bottom of a 6-quart slow cooker. Pour the blended salsa verde over the top. Add the remaining chicken broth, the drained and rinsed hominy, and the dried oregano. Stir gently to combine.

Cover the slow cooker and cook on low for 6-8 hours or on high for 4 hours, until the chicken is tender and cooked through.

Remove the chicken breasts from the slow cooker and place them on a cutting board. Use two forks to shred the meat. Return the shredded chicken to the slow cooker. Squeeze in the fresh lime juice and stir to combine. Season with salt and pepper to taste.

Ladle the posole into bowls and serve hot with your favorite toppings like sliced radishes, avocado, cilantro, and cotija cheese.