For the soup: Heat the oil in a large saucepan over medium-high heat. Add the onion and sauté until translucent, about 5 minutes. Pull the skin off the chicken thighs, sprinkle the chicken with salt and pepper. Add to the pan and cook until no longer pink, about 1 minute on each side. Add the broth and water. Bring the soup to a boil. Reduce the heat, cover and simmer until the chicken is cooked through, about 25 minutes.

Meanwhile, prepare the toppings of your choice.

Remove the chicken from the broth and place on a plate. Add the hominy to the broth and bring to a simmer. When chicken is cool enough to handle, pull the meat from the bones and shred the meat into bite sized pieces. Return the chicken to the soup with any juices on the plate. Add the salsa verde and bring to a simmer. Season to taste with salt and pepper.

Spoon the soup into bowls. Let each person garnishe with the toppings they like.