Season the pork shoulder pieces with salt, black pepper, and smoked paprika.
Heat a large skillet over medium heat and brown the pork in batches until the pieces develop color on all sides. Transfer the pork to the slow cooker.
In the same skillet, cook the onion and garlic for 3 to 4 minutes until softened, then add them to the slow cooker.
Pour the barbecue sauce and beef broth into the slow cooker and stir to combine with the pork and vegetables.
Cover and cook on low for 7 to 8 hours until the pork is very tender.
Stir in the frozen sweet corn and chopped collard greens. Continue cooking on low for 45 minutes to 1 hour until the greens are soft and the corn is heated through.
Taste and adjust salt or pepper if needed before serving.