Season the ribs. Pat the short ribs dry with paper towels. Sprinkle all sides with salt and pepper.
This helps build flavor and encourages browning.
Sear for color. Heat oil in a large skillet over medium-high. Sear the ribs in batches, 2–3 minutes per side, until well browned. Don’t overcrowd the pan.
Transfer to the slow cooker.
Soften the aromatics. In the same skillet, add onion, carrots, and celery with a pinch of salt. Cook 3–4 minutes, scraping up browned bits. Stir in garlic and tomato paste; cook 1 minute until fragrant.
Deglaze the pan. Pour in the red wine (or some broth) and simmer for 1–2 minutes to loosen the fond.
Pour everything into the slow cooker over the ribs.
Add liquids and herbs. Stir in beef broth, balsamic vinegar, Worcestershire sauce, thyme, and bay leaf. The liquid should come about halfway up the ribs.
Cook low and slow. Cover and cook on LOW for 7–9 hours or HIGH for 4–5 hours, until the meat is tender and pulls away from the bone easily.
Adjust seasoning. Remove the ribs and vegetables to a platter. Skim excess fat from the surface of the sauce.
Taste and adjust with salt, pepper, or a splash more balsamic if needed.
Thicken the sauce (optional). If you like a thicker gravy, mix 1–2 teaspoons of cornstarch with 1 tablespoon of cold water. Whisk into the hot sauce and simmer on HIGH in the slow cooker for 5–10 minutes until glossy.
Serve. Spoon the sauce over the ribs and garnish with chopped parsley. Serve with mashed potatoes, polenta, buttered noodles, or crusty bread.