In a bowl, mix cumin, oregano, salt, black pepper, and chili powder. Rub the seasoning blend evenly over the chicken.
Heat 1 tablespoon of olive oil in a skillet over medium-high heat. Sear the chicken on both sides until golden brown, then remove from the pan and set aside.
Add the remaining olive oil to the skillet. Sauté the diced onion until softened, then stir in the minced garlic and cook until fragrant.
Pour in the chicken broth (or beer), orange juice, and lime juice, scraping up any browned bits from the pan.
Return the chicken to the skillet, cover, and let it simmer for about 15 minutes or until fully cooked and tender.
Remove the chicken from the pan and shred it using two forks. Return the shredded chicken to the skillet, mixing it with the flavorful sauce.
Serve in warm tortillas, garnished with fresh chopped cilantro.