Scrub and dry the sweet potatoes. Place them whole in the slow cooker, making sure the lid closes completely.
Mix the brown sugar and cinnamon. Sprinkle over the potatoes, distribute the butter slices on top, and pour the apple juice into the spaces around them.
Cover and cook on low for 6 to 8 hours or high for 3 1/2 to 4 1/2 hours. A thin knife should slide easily through the largest potato. If firm, cook another 20 to 30 minutes.
Lift out the potatoes carefully. Split them, fluff the centers with a fork, and spoon the warm syrup over each serving.