Season the short ribs with kosher salt and pepper. Heat the oil in a large, heavy-bottomed pan (with a lid) over medium-high heat. Sear half of the ribs on all sides until well browned, 5-7 minutes each side. Transfer to a plate and repeat with the rest of the ribs. Wipe out any burned bits and drain all but 1 tablespoon of the fat from the pot.

Add the onion, carrot, celery, and garlic to the pot. Cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes. Stir in the tomato paste and cook for 2-3 minutes for the tomato paste to lose its raw taste. Use your fingers to crush the whole tomatoes straight into the pot, along with the liquid from the can. Add the red wine, beef broth, 1 ½ tablespoons rosemary, thyme, and bay leaves. Add the short ribs back to the pot. Bring to a boil, then reduce to a simmer and cover with a lid. Cook for 1 ½ hours, then uncover and simmer for another 1 ½ hours. The liquid will have reduced and thickened, and the meat should fall off the bone.

Spoon off any extra fat from the sauce, and serve with mashed potatoes, polenta, or pasta.