Toss the bones in oil and season them with a little salt and pepper. Roast the oxtail bones on a sheet pan at 375°F for 20 to 30 minutes or until they are dark brown, and start to 'sear' around the edges.
As the meat roasts, peel and rough chop the broth vegetables. This doesn't need to be pretty, they will simply add flavor to the oxtail broth, and are discarded once the broth is finished.
Once the oxtail bones are roasted, combine them with the chopped vegetables, thyme, garlic, bay leaf, peppercorns, red wine, and water. Place everything in a large pot and slowly bring the broth to a simmer.
Slowly let the oxtail broth simmer for about 4 hours. As the broth simmers you'll notice a white foam start to form on top of the liquid, skim it off as it forms. Keep an eye on the oxtail broth as it simmers to prevent it from boiling, it should just bubble along happily on the stove. Taste the broth occasionally to see how the flavor is developing, it should be rich and beefy.
Once the broth has a rich taste (after about 4 hours), you can safely turn the pot off. Strain the oxtail broth from the pot, and set aside the oxtail bones themselves.
Pick the meat of the oxtail, and reserve it for later. The broth can be cooled or kept warm if you plan on finishing the soup right away.
Finishing the oxtail soup
While the oxtail broth is simmering, medium dice the vegetable garnishes, and chop the herbs. Saute the vegetables in a pot with a little butter or oil, until they start to brown slightly.
Add the garlic and herb and cook for another minute or two. Once the vegetables start to brown, add the wine to de-glaze the pot. Add the oxtail broth, and picked oxtail meat to the pot. Bring the oxtail soup to a simmer and cook for another 30 minutes.
Taste the oxtail soup and season it with salt and pepper. Serve hot.
Notes
The oxtail soup can be served right away, or refrigerated and kept for up to a week. It makes a quick weeknight meal, re-heated on the stove top!