Heat the olive oil in a large skillet over medium heat and add the sausage, breaking it into crumbles as it cooks. Let it brown for about 5 to 7 minutes until it's cooked through and no longer pink. This step builds a deeper flavor than just dumping raw sausage straight into the crockpot.
Transfer the browned sausage into your slow cooker, then add the diced onion, minced garlic, cubed sweet potatoes, thyme, rosemary sprig, and adobo seasoning. Pour the chicken broth over everything so it's mostly submerged, then give it a quick stir to combine.
Cover the crockpot and cook on low for 6 hours or on high for about 3 hours, until the sweet potatoes are completely fork-tender. Resist lifting the lid too often, since every peek lets out heat and adds extra cooking time.
About 15 minutes before serving, stir in the torn kale leaves and let them wilt right in the hot broth. Remove the rosemary sprig, then stir in the apple cider vinegar and coconut milk or dairy-free cream if you're using it.
Give the soup a final taste and adjust the salt and pepper as needed. Ladle it into bowls while it's hot, and it's ready to enjoy straight away or portioned out for the week ahead.