Rub Cajun seasoning into the pork shoulder. Put pork shoulder into a slow cooker crock.
Pour jar of giardiniera with liquid over the pork. Sprinkle adobo seasoning over the pork and top with onion, cilantro, and garlic. Pour enough beer into the crock so the bottom half of the roast is submerged.
Cook on Low until the roast is falling apart, 6 to 8 hours. Shred the pork with a pair of forks in the slow cooker and stir with the liquid.