Heat a large, heavy pot over medium-high heat. Add a drizzle of olive oil and sear the beef short ribs for about 4-5 minutes on each side until well-browned.

Remove the seared short ribs and set aside. In the same pot, add chopped onion and carrot; cook for 3-4 minutes until softened. Add minced garlic and sauté for another minute.

Pour in one cup of red wine, scraping the bottom of the pot to release browned bits. Simmer for about 2-3 minutes to reduce slightly.

Stir in beef broth, tomato paste, bay leaf, and herbs. Bring to a simmer and return the short ribs to the pot. Cover and let simmer on low for 3-4 hours or until tender.

If possible, transfer pot to a preheated oven at 300°F (150°C) for extra tenderness, or use a slow cooker set on low for 6-8 hours.

While the ragu cooks, peel and chop potatoes. Boil in salted water for 15-20 minutes until fork-tender. Drain and return to pot; mash with butter and Parmesan until creamy.

Once the short ribs are tender, shred the meat, discarding the bones. Stir shredded meat back into the sauce and serve over the mashed potatoes.