In a food processor or high duty blender, add tomatillos, onion, both chiles, garlic, and cilantro and pulse/blend until everything is completely smooth with no chunks.
Add oil to a medium sized pot over medium heat. Pour green puree in pot along with 1 cup of chicken stock. Whisk together and season with salt and pepper.
Allow puree to cook, occasionally stirring, until it turns a darker green color. This can take up to 15 minutes.
While puree cooks, add remaining chicken stock and water to a larger pot over medium heat.
Once puree is dark green, whisk it into the liquid in the larger pot.
Next add shredded chicken breasts and drained hominy and stir together until well combined. Season with salt and pepper to taste.
Cook soup over medium heat until heated throughout then serve.
Garnish pozole with traditional toppings like avocado, lime wedges, radishes and cilantro if desired.