Step 1: Prepare the Beef Shanks

1. Pat the beef shanks dry with paper towels to remove excess moisture. This helps them brown evenly.
2. Season the shanks with salt and pepper, then dredge them lightly in flour, shaking off the excess.

Step 2: Sear the Shanks

1. Heat 2 tablespoons of olive oil in a large Dutch oven or heavy-bottomed skillet over medium-high heat.
2. Add the beef shanks and sear for 4-5 minutes per side, or until golden brown. Work in batches if necessary to avoid overcrowding the pan. Remove the shanks and set them aside on a plate.

Step 3: Sauté the Vegetables

1. Add the remaining tablespoon of olive oil to the pot. Lower the heat to medium and add the onion, carrot, and celery. Cook for 5-7 minutes, stirring occasionally, until softened.
2. Add the garlic and cook for another minute, being careful not to burn it.

Step 4: Deglaze the Pot

1. Pour in the white wine, scraping the bottom of the pot with a wooden spoon to release any browned bits.
2. Let the wine simmer for 2-3 minutes to reduce slightly.

Step 5: Build the Braising Liquid

1. Stir in the diced tomatoes, tomato paste, and beef broth. Add the thyme, bay leaf, and rosemary.
2. Return the seared shanks to the pot, nestling them into the liquid. The liquid should come about halfway up the sides of the shanks.

Step 6: Braise the Osso Buco

1. Bring the mixture to a gentle simmer, then cover the pot with a lid and transfer it to a preheated oven at 325°F (160°C).
2. Braise for 2-2 1/2 hours, or until the beef is fork-tender and the marrow is soft. Check occasionally and add more broth if needed.

Step 7: Make the Gremolata

1. In a small bowl, mix the lemon zest, parsley, and minced garlic. Set aside for garnishing.

Step 8: Serve the Osso Buco

1. Remove the pot from the oven and discard the bay leaf and rosemary sprig.
2. Serve the beef shanks with generous spoonfuls of the sauce, topped with gremolata for brightness. Pair with your favorite side dish.