Preheat your oven to 350°F (175°C).

In a large dutch oven or stock pot, heat the vegetable oil over medium-high heat. Brown the short ribs on all sides until caramelized. Do this in batches to avoid overcrowding. Once browned, set the ribs aside.

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

Stir in the tomato paste and sprinkle in the flour. Cook for a few minutes until the mixture thickens slightly.

Pour in the wine and simmer, scraping up the browned bits from the bottom of the pot.

Add the tomatoes with their juice, water, and break up the tomatoes with a spoon.

Return the short ribs to the pot, ensuring they are covered with liquid. Add more water if needed. Toss in parsley.

Simmer the ragu on the stove for a few minutes, then cover and transfer to the preheated oven. Bake for 2-3 hours until the beef is tender.

Remove the pot from the oven, strain the liquid into a sauce pot, and simmer to thicken, skimming fat periodically.

Shred the short ribs and add them back to the sauce.

For the mashed potatoes, boil the potatoes until fork-tender, then mash with butter. Add sour cream, parmesan, salt, and pepper.

Serve the beef ragu over the parmesan mashed potatoes. Garnish with parsley.