1. Preheat oven to 300°.
2. Heat a large Dutch oven over medium-high heat. Add oil to pan; swirl to coat. Add short ribs and oxtail to pan; cook 10 minutes, browning on all sides. Remove meat from pan; place on a plate.
3. Add onion, shallots, and garlic to pan; cook 3 minutes. Add tomato paste; cook 1 minute. Stir in wine; cook 2 minutes, scraping pan to loosen browned bits. Add meat, stock, and next 6 ingredients (through carrots); bring to a boil. Cover and bake at 300° for 2 hours or until beef is tender. Remove and discard bay leaves and thyme sprigs. Remove meat from bones; shred. Discard bones. Return shredded meat to pan; top with parsley and thyme leaves.