Cut the pork shoulder into large chunks, approximately 3 inches each. Pat the pieces dry with paper towels and season them with salt, black pepper, cumin, oregano, and smoked paprika.
Heat the olive oil in a large skillet over medium-high heat. Working in batches if necessary, brown the pork for several minutes on each side.
Add the browned pork to the slow cooker. Pour in the orange juice, lime juice, and chicken broth. Add the minced garlic, chipotle peppers, and a spoonful of adobo sauce. Scrape any browned bits from the bottom of the skillet so they become part of the sauce.
Add the lid to the slow cooker. Cook on high for 3-4 hours or low for 5-6 hours, or until the pork is extremely tender and easily pulls apart with a fork.
Transfer the pork to a large cutting board or baking sheet. Use two forks to shred it into bite-sized pieces. Skim excess fat from the cooking liquid if desired. Spoon some of the flavorful liquid over the shredded pork to keep it juicy.
Spread the shredded pork onto a large baking sheet. Drizzle with a little cooking liquid. Place under the broiler for approximately 3 to 5 minutes, or until the edges begin to brown and crisp. Toss the pork and broil for another 2 to 3 minutes if you want even more crispy pieces.
Squeeze fresh lime juice over the carnitas and serve with warm tortillas, cilantro, diced onion, avocado, salsa, or your favorite toppings.