In a large pot or Dutch oven, heat the olive oil over medium-high heat. Season the short ribs with salt and pepper, then sear them on all sides until browned. Remove and set aside.
In the same pot, add the diced onion, carrots, and celery. Sauté for about 5 minutes until softened. Add the minced garlic and cook for another minute.
Pour in the red wine, scraping the bottom of the pot to deglaze. Let it simmer for about 2-3 minutes.
Add the crushed tomatoes, beef broth, oregano, thyme, bay leaves, and the seared short ribs back into the pot. Bring to a boil, then reduce the heat to low. Cover and let it simmer for 2-3 hours until the meat is tender and falls off the bone.
While the ragu is cooking, prepare the mashed potatoes. Boil the cubed potatoes in salted water until fork-tender, about 15-20 minutes. Drain and return to the pot.
Add the butter, heavy cream, and Parmesan cheese to the potatoes. Mash until smooth and creamy. Season with salt and pepper to taste.
Once the short ribs are done, remove them from the pot. Shred the meat and discard the bones. Return the shredded meat to the sauce and stir to combine.
Cook the pasta according to package instructions. Drain and toss with the ragu. Serve the ragu over the pasta with a side of Parmesan mashed potatoes.