Place oxtail in a shallow dish. Combine soy sauce, Worcestershire sauce, salt, sugar, garlic and herb seasoning, browning sauce, paprika, cayenne pepper, and black pepper together in a small bowl. Rub both sides of oxtail with soy sauce mixture; discard any excess.

Heat vegetable oil in a large, deep skillet over medium-high heat. Sear oxtail in hot oil until golden brown, about 3 minutes per side; transfer to a plate and set aside.

Sauté carrots, celery, onion, and garlic in the same skillet until softened, about 5 minutes. Add beef broth, thyme, rosemary, and bay leaf; bring to a boil. Add oxtail, with its juices, and butter. Reduce heat to low, cover, and simmer until oxtail is fork tender, about 3 hours.

Uncover skillet and increase heat to high. Cook, stirring occasionally, until sauce reduces and thickens, about 5 minutes.