In a large bowl, toss the short rib pieces with the flour until each piece is coated.
Heat the oil in a large dutch oven over medium-high heat. Add the meat and brown on all sides, working in batches until complete. Discard excess oil, but do not scrape off the browned bits at the bottom (reserve them in the pan).
Add the meat back to the dutch oven with the red wine. Bring to a boil and cook until the liquid is reduced by half, approximately 8-10 minutes. Add the beef stock and simmer on low until the meat is tender, approximately 2 hours.
Skim the fat off the top and add the carrots, onion, mushrooms, thyme, oregano, and bay leaves. Continue to cook on low until the vegetables are tender, approximately 30 to 35 minutes. Season to taste with salt and pepper. Be sure to pick out the bay leaves before serving!
Serve warm over cooked egg noodles or mashed potatoes.