Preheat Oven: Preheat your oven to 325°F (160°C).

Prepare the Short Ribs: Pat the short ribs dry with paper towels and season them generously with salt and black pepper.

Brown the Ribs: Heat the olive oil in a large oven-safe Dutch oven or heavy-bottomed pot over medium-high heat. Add the short ribs and sear on all sides until browned, about 3-4 minutes per side. Remove the ribs from the pot and set them aside.

Sauté Vegetables: In the same pot, add the chopped onion, carrots, and celery. Cook for about 5 minutes, stirring occasionally, until the vegetables are softened. Add the minced garlic and cook for an additional minute until fragrant.

Deglaze the Pot: Pour in the red wine and use a wooden spoon to scrape up any browned bits from the bottom of the pot. Bring the wine to a simmer and cook for about 5 minutes to reduce slightly.

Add Remaining Ingredients: Stir in the beef broth, tomato paste, fresh thyme, and bay leaf. Return the short ribs to the pot, making sure they are partially submerged in the liquid.

Braise in the Oven: Cover the pot with a lid and transfer it to the preheated oven. Braise the short ribs for 2.5 to 3 hours, or until the meat is tender and easily pulls away from the bone.

Thicken the Sauce (Optional): If you prefer a thicker sauce, remove the cooked short ribs from the pot and cover them to keep warm. Mix the flour with the cold water to create a slurry and stir it into the sauce. Simmer on the stovetop for a few minutes until the sauce thickens. Return the short ribs to the pot and coat them with the sauce.

Garnish and Serve: Garnish with chopped fresh parsley before serving. Pair with mashed potatoes, polenta, or crusty bread to soak up the delicious sauce.