Preheat oven to 350°F.

Heat the vegetable oil over medium-high heat in a large dutch oven or stock pot. Add the short ribs and brown them on all sides until caramelized. Remove the ribs from the pot and set aside.

Reduce the heat to medium and add the diced carrots, celery, and onion. Cook for about ten minutes until the vegetables have softened. Add the garlic and cook for another couple of minutes.

Stir in the tomato paste until all of the veggies are coated. Sprinkle in the flour and stir to coat all of the vegetables. Continue to cook for another few minutes.

Pour in the wine and increase the heat until the pot begins to simmer. Deglaze the pot by scraping the bottom with the spatula.

Add the tomatoes and all of the juice from the can. Pour in 2 cups of water and stir. Break up the tomatoes with a wooden spoon or spatula.

Add the short ribs back to the pot, ensuring they are completely covered by the liquid. Toss in the parsley and stir.

Bring the pot to a strong simmer and then cover it, remove it from the heat, and transfer it to the preheated oven. Let it simmer for 2 to 3 hours or until the beef is fork-tender.

Once the beef is fork-tender, remove the pot from the oven. Remove the short ribs from the pot and set aside. Strain the liquid into a large sauce pot, pressing on the solids to extract the liquid.

Bring the sauce to a simmer over medium-high heat and let it thicken and reduce for at least 30 minutes, skimming the surface to remove the fat. Shred the short ribs and add them back to the thickened sauce.

Fill a large pot with water and bring it to a boil. Add the potatoes and boil until fork-tender.

Drain the potatoes and return them to the pot. Add the butter and mash the potatoes until creamy. Stir in the sour cream and Parmesan cheese, and season with salt and pepper.

Serve the ragu over the parmesan mashed potatoes, garnished with chopped parsley if desired.