In a large Dutch oven or saucepot set over medium heat, heat the oil. Add the onion and cook until translucent and fragrant, about 8 minutes. Add the garlic and cook for 3 to 4 more minutes. Add the oregano, coriander and cumin, and cook until slightly darkened and fragrant, 2 to 3 minutes. Add the green chiles, chopped tomatoes, salsa verde and cook until it just comes to a boil, about 2 minutes. Add the hominy and chicken broth and return to a boil. Reduce the heat to medium and simmer for at least 10 minutes to allow flavors to develop. Season with salt and pepper. Add chicken and cook until heated through, 3 minutes.
To serve, divide among 4 bowls and garnish as desired.