Cook the sausage in a 10-inch skillet over medium-high heat until it's well browned, stirring often to separate meat. Pour off any fat.
Stir the sausage, stock, black pepper, carrots, celery and beans in a 5-quart slow cooker.
Cover and cook on LOW for 7 to 8 hours.*
Stir in the tomatoes. Cover and cook for 1 hour or until the beans are tender. Sprinkle with the cheese.
*Or on HIGH for 4 to 5 hours.