Combine chili powder, oregano, paprika, cumin, and salt in a small mixing bowl. Set 1 1/2 teaspoons of spice mixture aside. Chop pork into bite-size pieces and coat with remaining spice mixture.
Chop onion and bell pepper, mince garlic, and set aside separately.
Heat 2 teaspoons oil in a large pot over medium-high heat. Add pork and cook for 5 minutes, allowing to brown while stirring occasionally. Remove and set aside.
Add remaining 1 teaspoon of oil to pan. When hot, add onion, bell pepper, and garlic, and sauté for 5 minutes, stirring occasionally. Return pork to pot along with the reserved spice mixture, broth, and drained hominy and tomatoes. Bring to a boil, then cover, reduce heat, and simmer for 25 minutes.
Serve with sliced apples on the side.