In a large heavy-bottomed pot, heat 2 tablespoons of olive oil over medium-high heat. Season the beef short ribs with salt and pepper, then sear them in the pot for about 10 minutes, turning occasionally until they are golden brown on all sides. Once browned, remove the ribs from the pot and set aside.

In the same pot, add your chopped onion, carrots, and celery, stir-frying them for 5 to 7 minutes. Cook until the vegetables soften and become fragrant, then add the minced garlic and cook for an additional minute.

Stir in 2 tablespoons of tomato paste, cooking it for 2 to 3 minutes until it darkens slightly. Next, add in the crushed tomatoes and beef broth, scraping up any browned bits from the bottom of the pot. Incorporate the fresh thyme, rosemary, and bay leaf, then return the short ribs to the pot.

Cover the pot and reduce the heat to low, letting the ragu simmer gently for 3 to 4 hours.

After simmering, remove the short ribs from the pot and let them cool slightly. Using two forks, shred the meat from the bones and return the tender, shredded beef to the pot.

Place 2 cups of peeled and chopped potatoes into a large pot, covering them with salted water. Bring to a boil and cook until the potatoes are tender, about 15-20 minutes. Drain and return potatoes to the pot; add butter, milk, and grated Parmesan, mashing until creamy.

Taste and season the mashed potatoes with salt and pepper. Serve by spooning creamy Parmesan mashed potatoes onto each plate and ladling the cozy short rib ragu on top.