Pat the short ribs dry with paper towels. Trim any excessive fat if desired but leave a thin layer for flavor. Season all sides generously with the kosher salt and freshly ground black pepper. Lightly dust each rib with the all-purpose flour, shaking off excess—this helps with browning and thickens the braising liquid slightly.

Braising Base

Preheat and brown

Preheat the oven to 325°F (160°C). In a large heavy-bottomed Dutch oven or ovenproof pot, heat the vegetable oil over medium-high heat until shimmering. Add the short ribs in a single layer (work in batches if necessary) and brown on all sides, about 3–4 minutes per side, until a deep mahogany color forms. Transfer browned ribs to a plate and set aside.

Sauté aromatics

Lower heat to medium. Add the butter to the pot. When melted, add the chopped onion, carrots, and celery. Cook, stirring occasionally, until the onion is translucent and vegetables begin to caramelize, about 6–8 minutes. Add the smashed garlic and cook 30–60 seconds until fragrant. Stir in the tomato paste and cook 1–2 minutes, stirring constantly, to remove the raw tomato flavor and develop color.

Deglaze

Pour in the dry red wine and use a wooden spoon to scrape any browned bits (fond) from the bottom of the pot. Bring the wine to a gentle boil and reduce until it has reduced by about half, 4–6 minutes. This concentrates flavor and burns off alcohol.

Add stock and herbs

Return the browned short ribs and any accumulated juices to the pot, nestling them into the vegetables. Add the beef stock until the ribs are about two-thirds submerged (approximately 3 cups). Stir in the bay leaves, thyme sprigs, rosemary (if using), and Worcestershire sauce. Bring the liquid to a gentle simmer on the stovetop.

Braise in oven

Cover the pot with a tight-fitting lid and transfer to the preheated oven. Braise until the short ribs are fork-tender and the meat is nearly falling off the bone, 2.5–3 hours depending on size. Check once halfway through to ensure the liquid is simmering gently; if the surface is dry, add a few tablespoons of stock or water.

Finishing

Reduce sauce and finish

Once ribs are tender, carefully transfer the ribs to a warm plate and tent with foil. Skim any excess fat from the surface of the braising liquid with a spoon or use a fat separator. Place the pot on the stovetop over medium-high heat and simmer the sauce until it reduces and thickens slightly, about 8–12 minutes. Taste and adjust seasoning with salt and pepper as needed. Stir in the red wine vinegar or lemon juice to brighten the sauce.

Serve

Return the short ribs to the sauce to warm briefly or spoon the sauce over the ribs on individual plates. Sprinkle chopped fresh parsley over the ribs for color and freshness. Serve over mashed potatoes, polenta, buttered noodles, or creamy parsnip purée to soak up the sauce.