Heat the olive oil in a skillet over medium-high heat. Season the pork shoulder with salt and pepper, then sear it on all sides until browned (about 3-4 minutes per side). Transfer the pork to the crockpot.
In the same skillet, add the diced onion and garlic. Sauté for 2-3 minutes until softened, then pour in the chicken broth, barbecue sauce, apple cider vinegar, smoked paprika, cumin, and chili powder. Stir to combine and bring to a simmer.
Pour the sauce mixture over the pork in the crockpot. Cover and cook on low for 8 hours or high for 4 hours, until the pork is tender and easily shredded with a fork.
Once cooked, remove the pork from the crockpot and shred it using two forks. Return the shredded pork to the crockpot and stir to combine with the sauce. Let it sit on warm for 10-15 minutes.
To assemble the bowls, divide the cooked brown rice or quinoa among serving bowls. Top with pulled pork, corn, black beans, diced tomatoes, and avocado slices. Garnish with fresh cilantro and serve with lime wedges on the side.