Place oxtails, sweet potatoes, bell pepper, onion, and garlic in a 6-quart slow cooker. Pour tomatoes and beef broth on top. Mix in brown sugar, chili powder, salt, pepper, cinnamon, allspice, and bay leaves.
Cover and cook on high for 5 to 6 hours, stirring occasionally.
Remove oxtails from the slow cooker. Shred meat off the bones; discard bones.
Skim fat off the top of the liquid in the slow cooker. Add meat back to the slow cooker. Taste and adjust levels of brown sugar, salt, and pepper. Stir to combine. Serve warm, topped with parsley.