Directions

• Pat dry oxtail with paper towels then sprinkle all over with 1 teaspoon each of the salt and pepper. Place flour in a wide shallow bowl. Dredge oxtail in flour, and shake off excess. Transfer oxtail to a large plate.
• Heat oil in a large Dutch oven over medium-high. Working in 2 batches, add oxtail, and cook until browned on 2 sides, 2 to 5 minutes per side. Remove from heat. Transfer browned oxtail to a plate. Clean Dutch oven.
• Place bacon in Dutch oven. Cook, stirring occasionally, over medium-high until bacon is browned and fat has rendered, 8 to 10 minutes. Add mushrooms, and cook, stirring occasionally, until mushrooms have released their water and are lightly browned all over, about 10 minutes. Reduce heat to medium. Add carrots and celery; cook, stirring often, until carrots are slightly softened, about 6 minutes. Add garlic, and cook, stirring constantly, until fragrant, about 1 minute. Add wine and vinegar; cook, stirring often, until just slightly thickened and reduced, 2 to 3 minutes. Add broth, and return oxtail to Dutch oven. Bring to a boil over high. Cover and reduce heat to low. Cook, stirring occasionally, until oxtail is tender but not falling off the bone, 1 hour, 30 minutes to 1 hour, 45 minutes.
• Remove from heat. Using a slotted spoon or kitchen tongs, transfer oxtail to a work surface, and let cool 15 minutes. While oxtail cools, skim and discard fat from surface of soup. Separate oxtail meat from bones; discard bones, and set meat aside. You should have about 1 1/3 cups of meat.
• Bring soup to a gentle boil over high. Stir in egg noodles and onions. Return to a simmer over medium, and cook, stirring occasionally, until noodles are tender, 6 to 8 minutes. Remove from heat. Stir in rosemary, mustard, picked oxtail meat, and remaining 3/4 teaspoon salt and 1/4 teaspoon pepper. Adjust seasoning to taste using additional salt and pepper, if desired. Divide soup evenly among bowls, and serve.