Place the chiles in a small pot of water, bring to a boil, reduce to a simmer and cook for 10 minutes or until chilis are softened.
Allow the chilis to cool to the touch and remove the seeds and stems with a sharp knife.
Place the chilis and 1/2 cup water from the pot into a blender or food processor and puree until smooth.
Place the chicken in a large stock pot with a the halved onions, garlic (unpeeled), bay leaves and 1 cup cilantro (stems and leaves). Cover with cool water. Cover with lid, bring to a boil, reduce to a simmer and cook for 35-40 minutes.
Heat a large skillet over medium heat, cover the bottom with a thin layer of olive oil and warm for 1-2 minutes. Pour in the chili puree and cook for 8 minutes or until it reduces and becomes darker in color and thickens.
Remove the chicken, cilantro, onion and bay leaf from the pot. Cool the chicken, remove the skin, bones, shred the chicken and add the meat back into the soup.
While the chicken is cooling, pour the chili puree, hominy and salt into the soup and simmer uncovered for 30-45 minutes. The longer you simmer, the thicker is will become.
Serve topped with additional chopped cilantro and other desired toppings.