Heat olive oil in a Dutch oven. Add oxtails and cook until browned, 3 to 5 minutes per side. Use tongs or a slotted spoon to transfer oxtails to a plate. Pour red wine into the Dutch oven; scrape any browned bits off the bottom with a wooden spoon.

Return oxtails to the Dutch oven and add vegetable broth. Bring to a boil. Simmer until flavors combine, about 90 minutes. Add 1 cup water, if needed, to keep the oxtails covered.

Add beef broth, barley, garlic, bay leaves, hot sauce, salt, and pepper. Simmer until barley softens, about 30 minutes. Add carrots, shallots, and celery. Continue simmering until oxtails and carrots are tender, about 30 minutes more.