Mix together all the ingredients for the marinade except the green onions, in a large bowl.
Add the oxtails and green onions to the bowl and use a spoon to mix and coat the oxtails with the marinade.
Cover the bowl. Put the bowl in the fridge and let the meat marinade overnight.
When making the stew, take the oxtails out of the bowl and transfer onto a clean plate. Remove any green onions that are stuck to the oxtails and put them back in the bowl with any of the remaining marinade.
Heat 1 tablespoon of the oil in a large pan on the stove over medium heat. Saute the chopped onions and minced garlic in the pan until the onions are translucent (about 1 minute).
Remove the onion mixture from the pan. Pour the remaining 2 tablespoons of oil onto the pan. Once the oil is heated (this should take a few seconds), add the oxtails to the pan and brown them on each side; you might have to do this in batches. Add more oil to the pan if you're browning the oxtails in batches.
Once all sides of the meat have browned, remove the meat from the pan and set aside on a clean plate.
Pour 2 cups of the beef broth into the pan. Bring the broth to a boil and deglaze the pan by using a wooden spoon to scrape the brown bits from the bottom of the pan.
Place the oxtails in a slow cooker. Add the carrots, sauteed onions, and Scotch bonnet pepper to the oxtails. Pour the broth from the pan onto the oxtails as well as the reserved marinade left in the bowl.
Mix the cornstarch with the remaining ½ cup of beef broth in a bowl until the mixture is smooth. Mix in the ketchup to the cornstarch "sludge". Add this mixture as well as the thyme and bay leaves to the ingredients in the slow cooker.
Use a wooden spoon to gently mix all the ingredients in the slow cooker together.
Place the lid on the slow cooker. Set the temperature indicator on the slow cooker to low and the timer to 8 hours.
Drain and rinse the lima (butter) beans from the can an hour before the stew is done cooking. Add the beans to the oxtail stew and let the stew cook for the remaining hour.
Remove the thyme stems and bay leaves from the oxtail stew once the stew is done cooking. Serve the stew with Jamaican rice and peas or white rice.