Preheat Oven to 275ºF.
In large saucepot sweat carrots, onions and celery. Add the garlic, red wine and balsamic vinegar. Reduce by one-third. Add the veal stock, and bouquet garni. Allow to simmer.
In large fry pan, heat the vegetable oil. Season the oxtail with salt and pepper. Sear the oxtail on both sides until golden brown. Add more vegetable oil if needed.
Remove the oxtail and place it in the braising liquid. Bring back to a simmer and cover with a tight-fitting lid. Place in the preheated oven and allow to cook for 2-3 hours. The oxtail is done when the meat falls freely away from the bone.
In a large pot with boiling salted water, cook the pasta according to instructions on the package. When the pasta is al dente, strain, do not rinse with water. Add a small amount of olive oil to prevent pasta from sticking, and place on sheet pan to allow to air dry. Do not rinse.
When the oxtail is done, remove it from the braising liquid. Strain the liquid and transfer to a clean sauce pot. Reduce by one-half until it reaches a thick consistency. Check the seasoning. Pull the oxtail meat off of the bone.
Add pasta to the sauce and reheat. Add the oxtail meat and toss. Adjust the seasoning. Serve immediately