Pat oxtail dry and season with salt and pepper. Heat oil in a large skillet over medium-high heat and brown oxtail in 3 uncrowded batches for about 6 minutes each, transferring pieces to a 6-quart slow cooker.
Cook onion in the skillet for 4 minutes. Stir in garlic, ginger and tomato paste for 1 minute, then add broth and scrape up the browned bits.
Pour the skillet mixture into the cooker and add carrots, soy sauce, brown sugar, thyme and allspice. Cover and cook on low for 9 to 10 hours until oxtail reaches at least 145°F and the meat is very tender around the bones.
Lift oxtail carefully onto a plate and skim excess fat from the gravy. Check for and discard any loose bone fragments, leaving intact center bones in the oxtail pieces.
Mash 1/2 cup of the butter beans and stir into the gravy with the remaining whole beans. Return oxtail, cover and cook on high for 25 to 30 minutes until the beans are hot and the gravy coats a spoon.
Divide among 6 bowls, serving the oxtail with its intact bones and eating the meat around them.