Sear the Short Ribs: Pat the short ribs dry with paper towels and season generously with salt and pepper. Heat the olive oil in a large, heavy-bottomed Dutch oven over medium-high heat. Sear the short ribs in batches on all sides until deeply browned, about 3-4 minutes per side. Remove the short ribs from the Dutch oven and set aside.

Sauté the Vegetables: Add the onion, carrots, and celery to the Dutch oven and cook over medium heat until softened and lightly browned, about 8-10 minutes. Add the garlic and cook for 1 minute more until fragrant.

Deglaze the Pot: Pour in the red wine and bring to a simmer, scraping up any browned bits from the bottom of the pot.

Add Remaining Ingredients: Stir in the beef broth, tomato paste, Worcestershire sauce, rosemary, thyme, and bay leaf. Bring to a simmer.

Braise the Short Ribs: Return the short ribs to the Dutch oven, making sure they are mostly submerged in the liquid. Bring the liquid back to a simmer, then cover the Dutch oven tightly and transfer it to a preheated oven at 325°F (160°C). Braise for 3-3.5 hours, or until the short ribs are fork-tender.

Make the Sauce: Remove the short ribs from the Dutch oven and set aside. Strain the braising liquid through a fine-mesh sieve into a saucepan. Discard the solids. In a small bowl, whisk together the butter and flour to form a roux. Bring the strained braising liquid to a simmer over medium heat. Whisk in the roux and cook, stirring constantly, until the sauce has thickened to your desired consistency, about 5-7 minutes. Season with salt and pepper to taste.

Serve: Return the short ribs to the sauce and heat through. Serve the braised beef short ribs over mashed potatoes, polenta, or creamy risotto. Garnish with fresh parsley.