Start by heating 2 tablespoons of vegetable oil in a deep skillet. Add the chicken breasts and sear them on medium-high heat until no longer pink and the juices run clear. This takes about 20 minutes. Once they’re cooked, remove the chicken and set it aside to cool. Once cooled, shred the chicken using two forks or your hands.
Take the same skillet and add the remaining vegetable oil. Heat it over medium-high heat, then toss in the chopped onions and garlic. Stir and cook them for about 5 minutes until softened and aromatic.
Add the shredded chicken to the skillet with the cooked aromatics. Pour in the chicken broth, water, chili powder, salt, and oregano. Stir everything together and bring it to a gentle simmer. Cover the pot, lower the heat, and let it cook for 90 minutes.
After simmering, add the rinsed and drained hominy to the skillet. Cook for another 15 minutes until the hominy is tender. Taste your pozole and adjust the seasoning as needed. You can add more chili powder for some kick or a pinch of salt if required.
Ladle the pozole into bowls and serve it with a crisp tostada shell on the side. Garnish with your favorite toppings like shredded lettuce, chopped cilantro, diced onions, radishes, and a wedge of lime for that final burst of freshness.