1. Season ribs with 1/2 teaspoon salt and some pepper. Coat with cornstarch. Heat oil in a large heavy pot (preferably enameled cast iron) over medium-high heat. Lightly brown ribs on all sides, about 6 minutes. Transfer to a plate.
2. Add mushrooms to pot. Cook until browned, about 4 minutes. Transfer to a bowl; add cubed carrot.
3. Add shallots, celery, bacon, and chopped carrots to pot. Cook until caramelized, about 6 minutes. Stir in tomato paste.
4. Return ribs with plate juices to pot. Add thyme and bay leaf. Raise heat to high. Add wine. Cook, scraping up brown bits with a wooden spoon, until slightly reduced, about 1 minute. Add stock and water. Bring to a boil. Reduce heat, and simmer, partially covered, until beef is tender, 2 to 2 1/2 hours.
5. Remove ribs. Separate meat from bones; discard. Cut meat into bite-size pieces; return to pot. Add reserved mushroom-carrot mixture. Bring to a simmer; cook until cubed carrots are tender. Season with salt. Ladle soup over bowls of herbed egg noodles and serve with horseradish chive bread on the side.