Preheat the oven to 325 degrees F.

Adjust the racks to the middle-low position, leaving clearance for your pot.

Start by patting the beef shanks dry and seasoning all sides with salt.

Preheat a large Dutch oven or braiser over medium-high heat.

Add oil and swirl to coat.

Add the shanks, a few at a time, in a single layer and brown on both sides, 5 to 7 minutes.

Transfer to a platter and repeat with the remaining shanks until all are browned.

Reduce the heat to medium.

Add the onion and sautee for 3 minutes until just starting to soften.

Add the celery and carrot and sautee for another 5 minutes, until the onion has become translucent and all of the veggies are softened.

Add the garlic and cook 30 seconds longer.

Then, stir in the tomato paste to coat.

Carefully deglaze the pan by pouring in half of the wine, and scraping up the browned bits (the fond) at the bottom of the pan.

Add the remaining wine, beef stock, and tomatoes with the sauce.

Stir to mix everything together.

Add the thyme, rosemary and bay leaves.

Then nestle the beef shanks back into the pan.

Transfer the meat to a clean bowl.

Pull the meat from the bone, and discard fat and bones.

Using two forks, shred the meat.

Return the meat to the Dutch oven.

Add the balsamic vinegar and season with salt and pepper to taste.