Season & prep meat: Pat the short ribs thoroughly dry with paper towels. Season generously on all sides with kosher salt and cracked black pepper. Let sit at room temperature for 20 minutes.

Hard sear for deep fond: Heat olive oil in a heavy 6 to 8-quart enameled cast-iron Dutch oven over medium-high heat. Working in batches to avoid crowding, sear the ribs for 3 to 4 minutes per side until deeply browned and caramelized. Transfer seared ribs to a warm plate.

Caramelize aromatics: Pour off all but 2 tablespoons of rendered beef fat. Add diced onion, carrots, and celery to the pot. Sauté for 5 to 6 minutes until lightly browned. Stir in tomato paste and garlic halves, cooking for 2 minutes until the paste turns a deep brick-red.

Deglaze & build braise: Pour in the balsamic vinegar and 1 cup of beef bone broth, scraping up all the golden browned fond bits from the bottom with a wooden spoon. Pour in remaining broth, rosemary, thyme, and bay leaves.

Nestle & slow-braise: Return the seared short ribs and any resting juices back into the Dutch oven, nestling them bone-side down into the liquid (the meat should be about 2/3 submerged). Bring to a gentle simmer, cover tightly with the heavy lid, and transfer to a 325°F (165°C) oven for 2.5 to 3 hours until fork-tender.

Reduce gravy & serve: Carefully transfer ribs and braised carrots to a platter. Skim excess fat from the surface of the braising liquid. Simmer the remaining sauce over medium heat on the stovetop for 8 to 10 minutes until reduced to a velvety, glossy glaze. Spoon generously over ribs and serve hot over mashed potatoes!