Sear the Short Ribs: Preheat your oven to 325°F (163°C). Warm the olive oil in a spacious, sturdy Dutch oven set over medium-high heat. Pat the short ribs dry with paper towels and generously season them with kosher salt and black pepper. Lightly dust each rib with flour. Once the oil is hot, sear the short ribs on all sides until browned, about 3-4 minutes per side.

Sauté the Vegetables: In the same pot, incorporate the chopped carrots, celery, and onion. Sauté for 5 to 7 minutes, stirring occasionally, until the vegetables become tender. Then, add the garlic and continue to cook for another minute, allowing its aroma to enhance the dish.

Add Tomato Paste and Wine: Stir in the tomato paste and cook for 2-3 minutes to allow the flavors to deepen. Slowly pour in the red wine, scraping up any browned bits from the bottom of the pot. Let the wine simmer for about 5 minutes to reduce slightly.

Add Stock and Herbs: Add the beef stock, bay leaves, rosemary, thyme, and the optional parmesan rind. Return the seared short ribs to the pot, making sure they are mostly submerged in the liquid.

Braise in the Oven: Place the pot in the preheated oven and braise for 2.5 to 3 hours, or until the short ribs are tender enough to be easily pierced with a fork and the meat begins to separate from the bone. Check the ribs halfway through to ensure they are still submerged in liquid; add more beef stock or water if necessary.

Finish and Serve: Once the ribs are tender, remove the pot from the oven and discard the bay leaves, rosemary sprigs, thyme sprigs, and parmesan rind. Remove any surplus fat that has risen to the top of the braising liquid. Serve the short ribs with the braising sauce over mashed potatoes, polenta, or crusty bread.