Preheat your oven to 325°F (160°C). Pat the beef short ribs thoroughly dry with paper towels. Season generously all over with kosher salt and black pepper.

Heat the olive oil in a large Dutch oven over medium-high heat until shimmering. Carefully add the short ribs, working in batches if necessary to avoid overcrowding the pot. Sear on all sides until deeply browned, about 3-5 minutes per side. Remove the ribs from the pot and set aside on a plate.

Reduce the heat to medium. Add the chopped onion, carrots, and celery to the Dutch oven. Sauté, stirring occasionally, until softened and lightly browned, about 8-10 minutes. Add the minced garlic and tomato paste, stirring constantly for 1 minute until fragrant.

Pour in the red wine, scraping the bottom of the pot with a wooden spoon to deglaze and release any browned bits (fond). Bring to a simmer and let the wine reduce by about half, approximately 5-7 minutes.

Stir in the beef broth, Worcestershire sauce (if using), fresh rosemary, fresh thyme, and bay leaves. Bring the liquid back to a gentle simmer. Carefully return the seared short ribs to the Dutch oven, ensuring they are mostly submerged in the liquid. If not, add a little more beef broth or water.

Cover the Dutch oven tightly with its lid and transfer it to the preheated oven. Braise for 3 to 4 hours, or until the short ribs are fork-tender and practically falling off the bone. Check periodically to ensure liquid levels are adequate and the ribs aren't drying out.

Once tender, carefully remove the Dutch oven from the oven. Remove the short ribs from the pot and transfer them to a clean plate, tent loosely with foil to keep warm. Discard the rosemary, thyme, and bay leaves from the braising liquid.

For a smoother sauce, you can strain the braising liquid through a fine-mesh sieve, pressing on the solids to extract as much liquid as possible. Discard the solids. Skim any excess fat from the surface of the sauce. Return the sauce to the Dutch oven (or a saucepan) and simmer over medium heat, if desired, to thicken it slightly. Whisk in the cold butter, piece by piece, until melted and incorporated for a richer, glossier sauce.

Serve the braised beef short ribs immediately with the rich red wine sauce, garnished with fresh chopped parsley. They pair wonderfully with mashed potatoes, polenta, or crusty bread.