Mix brine ingredients in a large, deep bowl or stockpot. Immerse pork, refrigerate and let marinate for 24 hours.
Pour 2 tablespoons oil into a large frying pan on medium-high heat. Remove pork from brine and pat dry. Salt and pepper, then brown all sides.
While pork is browning, place remaining 2 tablespoons oil in another large, deep pan and heat on medium-high heat. Add onion and garlic and sauté for 5 minutes. Add cilantro and cumin seeds, and cook another 3-4 minutes. Add all other ingredients, including the seared pork. Cover. Simmer on low heat for 2 hours, turning pork every 30 minutes. Uncover. Cook another hour or until pork is tender enough to pull apart with a fork. Remove from pan and shred into bite-sized chunks. Strain liquid into a stockpot, add pork and stir.
To serve, place pork in warmed tortillas. Garnish with pico de gallo and avocado.
Makes 10 servings. Can be doubled for large groups.