In a large Dutch oven, heat 2 tablespoons of olive oil over medium-high heat. Season the short ribs generously with salt and pepper, then add them to the pot in batches. Brown the ribs on all sides for about 10 minutes until they develop a rich, golden crust.

Once the ribs are browned, remove them and set aside. In the same pot, add chopped onion, carrots, and celery; cook for 5-7 minutes until softened. Add minced garlic and sauté for an additional minute.

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

Cover the Dutch oven and reduce heat to low, allowing to simmer. Braise gently for 3-4 hours, stirring occasionally until the ribs are fork-tender.

Once tender, remove ribs from pot and shred the meat, discarding excess fat and bones. Return shredded meat to the pot, stir to combine, and adjust seasoning with salt and pepper.

Peel and chop russet potatoes. Boil in salted water for about 15-20 minutes until fork-tender. Drain and return to pot. Add butter, milk, and parmesan cheese; mash until creamy and smooth.

Serve by layering creamy parmesan mashed potatoes and topping with short rib ragu. Garnish with fresh parsley and additional parmesan cheese.