Remove short ribs from the refrigerator 30 minutes before cooking, then pat every surface completely dry with paper towels. Season all sides generously with kosher salt and black pepper, then set aside. Preheat your oven to 325°F (165°C).
Heat a Dutch oven over medium-high heat for 2 minutes, then add the oil and heat until shimmering. Working in batches of 2–3, sear the ribs fat-side down first for 3–4 minutes per side until a deep golden-brown crust forms on all sides; transfer to a plate and repeat with remaining ribs. Pour off all but 2 tablespoons of fat, leaving the browned fond in the pot.
Reduce heat to medium and add the onion, carrots, and celery to the pot; cook for 8–10 minutes until softened. Add the garlic and cook 1–2 minutes more, then push vegetables aside, add the tomato paste to the center, and cook for 2–3 minutes until it darkens to a deep brick red. If using flour, sprinkle it over the vegetables and stir to combine.
Increase heat to medium-high and pour in the entire bottle of red wine, scraping up all the browned bits from the bottom of the pot. Stir in the Worcestershire sauce and let the wine boil and reduce by half, about 10–12 minutes.
Pour in the beef broth and stir to combine, then add the thyme, rosemary, and bay leaves. Nestle the seared short ribs back into the pot meat-side down, ensuring the liquid comes about halfway up the sides of the ribs. Bring to a simmer over medium heat.
Cover the Dutch oven tightly and transfer to the preheated 325°F (165°C) oven. Braise undisturbed for 2.5 to 3 hours, until the meat is completely tender and a fork slides in with virtually no resistance; if still firm, return to the oven for another 30 minutes.
Remove the ribs and set aside loosely tented with foil. Strain the braising liquid through a fine mesh strainer into a saucepan, discarding the solids, then skim excess fat and simmer over medium-high heat for 10–15 minutes until reduced to a glossy, sauce-like consistency. Season to taste with salt and pepper.
Return the ribs to the Dutch oven or a serving dish and ladle the finished sauce generously over the top. Sprinkle with chopped fresh parsley and serve immediately over mashed potatoes, polenta, or egg noodles.