In a large skillet or pot, cook sausage over medium heat while breaking into pieces. Once brown, remove with a slotted spoon and drain on a plate lined with paper towels. Drain fat from pan, leaving about 1 tbsp.
Cook garlic, onion, carrots and celery in reserved fat for 4-5 minutes or until fragrant.
Transfer veggies into a slow cooker, add stock, pepper, salt and stir in sausage.
Cover and cook on high for 3 hours or low for 6 hours. Add kale to the slow cooker about 10 minutes before serving.
Portion soup into bowls, season with additional salt and pepper.