Pat the short ribs dry with paper towels. Season all sides generously with kosher salt and black pepper. Place the flour on a plate and lightly dredge each short rib, shaking off any excess.

Heat the olive oil in a large skillet or Dutch oven over medium-high heat. Once the oil is shimmering, carefully place the short ribs in the skillet, ensuring not to overcrowd the pan (work in batches if necessary). Sear for 2-3 minutes per side, until a deep brown crust forms. Transfer the seared ribs to the basin of your slow cooker.

Reduce the skillet heat to medium. Add the chopped onion, carrots, and celery to the same skillet, using the rendered fat from the ribs. Sauté for 5-7 minutes, or until the vegetables have softened. Add the minced garlic and tomato paste, and cook for another minute until fragrant, stirring constantly.

Pour the red wine and balsamic vinegar into the skillet to deglaze, scraping up any browned bits from the bottom of the pan with a wooden spoon. Let the liquid simmer and reduce by about half, which should take 3-5 minutes.

Stir in the beef broth, Worcestershire sauce, bay leaves, and fresh thyme sprigs. Bring the mixture to a gentle simmer.

Carefully pour the braising liquid and vegetable mixture over the short ribs in the slow cooker. Ensure the ribs are mostly submerged. Secure the lid.

Cook on LOW for 7-8 hours or on HIGH for 4-5 hours. The short ribs are done when they are fork-tender and falling off the bone.

Gently remove the cooked short ribs from the slow cooker and place them on a platter; tent with foil to keep warm. Let the cooking liquid sit for a few minutes, then skim any excess fat from the surface with a spoon.

Pour the remaining liquid and vegetables through a fine-mesh sieve into a medium saucepan. Discard the solids in the sieve. (For a more rustic sauce, you can skip straining).

Bring the sauce to a simmer over medium heat. If you'd like a thicker sauce, whisk together the cornstarch and cold water in a small bowl to create a slurry. Slowly pour the slurry into the simmering sauce, whisking continuously until it thickens, about 1-2 minutes. Taste and adjust seasoning with salt and pepper if needed.

Serve the warm short ribs immediately, generously spooning the rich sauce over the top. Garnish with fresh chopped parsley. This dish is excellent served over creamy mashed potatoes, polenta, or egg noodles.