Transfer the chicken breasts onto a large cutting board and carefully slice them in half so you have thinly sliced pieces. Sprinkle them on both sides with salt and pepper.
Heat a tablespoon of oil in a skillet over medium-high heat. Add the chicken breast in a single layer and sear for 1 minute on both sides until golden brown. Turn the heat to low, cover the pan, and cook for 12 minutes more, flipping the chicken halfway to full cook. Once cooked, set the chicken aside.
Add the chicken broth to a medium Dutch oven and bring it to a rapid simmer. Once simmering, add the bay leaf, thyme, oregano, garlic, cumin, 1/2 teaspoon of the salt, chili powder, coriander, and red pepper flakes. Reduce the heat to low and simmer for 15 minutes.
Using 2 forks, shred the chicken into small pieces. Add the chicken and drained hominy to the Dutch oven. Raise the heat to medium to warm everything through. Taste and add more salt or other seasonings if needed. Discard the bay leaf.
Serve the soup in individual bowls with any of the desired toppings.