Pat the oxtails dry, then season with the kosher salt and black pepper. Drizzle with Worcestershire sauce and toss to coat. Sprinkle with 1/4 cup flour and turn until evenly coated.
Heat the vegetable oil in a large skillet over medium heat. Working in batches, brown the oxtails well on all sides, then transfer them to the slow cooker.
Check the oil for burned bits. If necessary, carefully strain the oil and return it to the skillet. Gradually whisk in the remaining 1 cup flour.
Cook the flour mixture over medium heat, whisking continuously, until deep brown and the consistency resembles chunky peanut butter.
Slowly whisk in the beef broth, making sure the gravy stays smooth and lump-free. Increase the heat and bring to a full boil.
Reduce the heat to medium. Stir in the sliced onion and garlic, then season the gravy to taste with additional salt and pepper.
Pour the gravy over the oxtails, making sure they are well covered. Cover and cook on Low for about 8 hours, or on High for 4 to 5 hours, until the meat is fork-tender.
Skim excess fat from the gravy if desired. Serve the smothered oxtails hot with mashed potatoes or rice.