Heat 2 tablespoons of olive oil in a large Dutch oven over medium-high heat. Season the short ribs with salt and pepper, and brown them on all sides for about 10 minutes. Remove and set aside.

Add chopped onions, carrots, and celery to the pot, sautéing for 5-7 minutes until softened. Stir occasionally. Add minced garlic and sauté for another minute.

Stir in 2 tablespoons of tomato paste and cook for 2-3 minutes. Pour in crushed tomatoes and beef broth, scraping the bottom of the pot. Bring to a simmer.

Add fresh thyme, rosemary, and a bay leaf. Return the browned short ribs to the pot and cover. Reduce heat and let simmer for 3-4 hours.

Remove ribs, shred the meat, and return it to the sauce. Adjust seasoning with salt and pepper.

In another pot, boil salted water. Add peeled and chopped potatoes and cook for 15-20 minutes until fork-tender. Drain, then return to the pot.

Add butter and milk to the potatoes and mash until smooth. Stir in grated Parmesan cheese and season to taste.

Plate the creamy mashed potatoes and top with the short rib ragu. Optionally garnish with parsley and more Parmesan.