Preheat your oven to 300°F (150°C).
In a small bowl, combine the sea salt, black pepper, ground cumin, dried oregano, and cayenne pepper to make the spice rub.
Pat the pork chunks dry with paper towels and coat them thoroughly with the spice rub.
In a large Dutch oven, heat the olive oil over medium-high heat. Add the pork chunks in batches, searing them until browned on all sides, about 2-3 minutes per side. Remove the pork and set aside.
In the same Dutch oven, sauté the chopped onion and minced garlic until translucent and fragrant, about 3 minutes.
Deglaze the pot with the chicken broth, scraping up any browned bits from the bottom.
Add the browned pork back into the Dutch oven. Pour over the orange juice and zest, and lime juice, and stir to combine.
Cover the Dutch oven with its lid and place it in the preheated oven. Cook for about 2.5 to 3 hours, or until the pork is tender and shreds easily.
Remove the Dutch oven from the oven and shred the pork using two forks, discarding any excess fat.
If desired, spread the shredded pork in a single layer on a baking sheet and broil for 3-5 minutes to crisp up the edges.
Serve hot, garnished with fresh cilantro and avocado slices if using.