1. Preheat your oven to 325°F (165°C).
2. Season the short ribs generously with salt and pepper on all sides.
3. Heat the vegetable oil in a large Dutch oven over medium-high heat. Once hot, sear the short ribs in batches until browned on all sides, about 3-4 minutes per side. Remove and set aside.
4. In the same pot, add the onion, carrots, and celery. Sauté until the vegetables are soft and beginning to caramelize, about 8 minutes.
5. Add the garlic and cook for another minute until fragrant.

1. Pour in the red wine to deglaze the pot, scraping up any browned bits from the bottom. Let the wine simmer and reduce by half, about 10 minutes.
2. Add the beef stock, thyme, and rosemary to the pot. Return the short ribs to the pot, ensuring they are mostly submerged in the liquid.
3. Bring the liquid to a simmer, then cover the pot with a lid and transfer it to the preheated oven. Braise for about 2.5 hours, or until the meat is fork-tender.

1. About 30 minutes before the short ribs are done, place the potatoes and garlic cloves in a large pot and cover with cold water. Add a generous pinch of salt.
2. Bring the water to a boil over high heat, then reduce to a simmer and cook until the potatoes are very tender, about 20 minutes.
3. Drain the potatoes and garlic well, then return them to the pot. Add the heavy cream and butter. Mash until smooth and creamy. Season with salt and pepper to taste.

1. Once the short ribs are done, remove them from the pot and strain the braising liquid through a fine sieve into a saucepan. Discard the solids.
2. Simmer the strained liquid over medium-high heat to reduce and thicken slightly, about 10 minutes.
3. Serve the short ribs over a generous scoop of garlic mashed potatoes. Drizzle some of the reduced sauce over the top and garnish with chopped parsley.
4. Enjoy your richly flavored Braised Short Ribs with Red Wine Reduction and Garlic Mashed Potatoes, a perfect American main course for a special occasion!