Rinse the oxtails with water and vinegar, then dry them very well with paper towels before seasoning with the brown sugar, soy sauce, Worcestershire Sauce, salt, garlic powder, black pepper, ground allspice, and browning. Rub the seasoning mixture over every piece until the oxtails look evenly coated and dark.

Set a 6-quart pressure cooker to High Sauté and heat the vegetable oil, then arrange the larger oxtail pieces flat side down with about ¼ inch between them. Brown the pieces on all sides until they develop a deep mahogany crust and release easily from the pot.

Transfer the browned oxtails to a bowl. Leave the browned bits and rendered flavor in the pressure cooker insert.

Pour about 2 Tablespoons of the beef broth into the hot insert and scrape the bottom with a wooden spatula, then add the yellow onion, green onions, carrots, garlic, and chopped pepper. Sauté for about 5 minutes, until the onions soften and the garlic and thyme-like aromatics smell fragrant.

Stir in the dried thyme, reserved oxtails and their seasoning liquid, remaining beef broth, and ketchup. The liquid should look deeply colored, with the browned bits fully loosened from the bottom.

Cancel the Sauté setting, lock the lid, and cook on high pressure for 45 minutes, then allow a full natural pressure release. The meat should feel yielding around the bone when pierced with a fork; avoid rushing the release.

Lift out the oxtails and vegetables, leaving the cooking liquid behind, then set the cooker to Sauté and bring the liquid to a simmer. Skim off any excess surface fat before thickening so the gravy tastes rich rather than oily.

Mix the cornstarch and water in a separate bowl, stir the slurry into the simmering liquid, then add the drained Butter Beans and simmer for about 5 minutes. The gravy is ready when it lightly coats the back of a spoon and the beans are warmed but still whole.

Return the oxtails and vegetables to the thickened gravy and turn them gently to coat. The finished braise should be glossy, deeply savory, and tender enough for the meat to pull easily from the bone.